Vol. 52, No. 1

Bagrinovsky K.A., Nikonova A.A., Sokolov N.A. (Moscow) Methods of technological transformation in productive system
Economics and mathematical methods
, 2016, 52 (1), 3-19.
Some adaptive approach to the management of technology modernization is proposed on microeconomic and mezoeconomic level. The mechanism is realized with the special methods and models, aimed to determining the best productive technologies and governance driving influences to shift the productive system to the new technologies in accordance with its internal specialties and the overall system resource’s restrictions. There is specificity in the key characteristics identified for productive system that affect mobility and adaptability. The opportunities for including some special structures and relationships in the economic system are discussed which will be able to contribute to harmonize the interests of economic agents, for example, in the framework both of formation of an appropriate corporate culture and of appropriate support from the macro-regulator. The set of economic-mathematical models of technological change is presented in the general scheme of technological transformation of productive system. Description follows with illustration for basic models both of formation of upgrade options; choice of new technologies and choice of management tools and incentive measures, taking into account some resource and price restrictions. Creation and approbation of the organizational and economic mechanisms to change technology and business environment are based on iterative procedures for mutual settings with different input parameters of productive system and its environment. So the decisions made in variable environment with the help of the new technology introduction mode suggested in such scheme will be in balance with essential technological and economic parameters.
Keywords: productive technology, productive factors (labor, capital), resource input, output, price, demand, supply, innovation, driving influences.
JEL Classification: C61, D24, O14.

Prokopyev M.G. (Moscow) Analysis of influence of food import prices on domestic market prices: methodical aspects
Economics and mathematical methods
, 2016, 52 (1), 20-27.
The article examines the impact of the prices of imported products in the domestic prices (producer prices and consumer prices) under conditions of imperfect substitution. Special attention is paid to the extent to which imported and domestic goods to replace each other in the domestic market. In this context, examines the relationship elasticity transmission prices for imported products in the domestic prices and the Armington elasticity of substitution. The research is based on a simple one-sector model of supply and demand, which is on the demand side includes the Armington approach. The relationship of the elasticities of substitution and elasticity of transmission price of imports in producer prices and consumer prices is illustrated by the example of the domestic market of meat (poultry, cattle and pork). The results do not contradict the economic reality and the situation on food markets.
Keywords: Import substitution, price of imports, the domestic price, elasticity of substitution, elasticity of transmission, Armington apðroximation, food market.
JEL Classification: F140.

Aivazian S.A., Afanasiev M.Yu., Kudrov A.V. (Moscow) Models of productive capacity and technological efficiency evaluations of regions of the Russian Federation concerning the output structure
Economics and mathematical methods
, 2016, 52 (1), 28-44.
Based on the author's methodology econometric model production potential of Russian regions is built, taking into account evaluation intellectual capital and the characteristics of the factors of efficiency, determining the willingness to innovate. In the development of the results which were presented by the authors in (Makarov et al., 2014), the estimates of technical efficiency of production for all regions for the period 2009–2013 were got. Econometric models of the production potential for groups of regions that are comparable in the structure of industrial production were built. The resulting estimates of technical efficiency for regions within each group were got. Hypothesis’ testing was conducted, which allows to compare estimates of the effectiveness of the region, obtained from the model with the relevant group the estimates based on the model constructed for the entire set of regions. It is shown that the increase in the elasticity of GRP by volume of intellectual capital is observed for the regions which are included into the base group, the “processing” and “agriculture” regions, and also in the model constructed for the entire set of regions. It is established that the model constructed for the entire set of regions, can be used to obtain local estimates of the efficiency of regions of the base group. Local evaluation of the efficiency of the regions in the other groups, it is advisable to obtain appropriate models. The General model of the production potential correctly describes efficiency’s time trends, which was estimated by model of production potential of the regions of each group. Therefore, the General model can be used to simulate the dynamics of regions’ efficiency.
Please note the figures of evaluating models' parameters in line 4 of Table 3 should be read without zero before the comma
Keywords: regional economy, econometric modeling, hypothesis testing, stochastic frontier, efficiency estimation.
JEL Classification: C12, C51, R15.

Gavrilets Yu.N., Klimenko K.V., Kudrov A.V. (Moscow) Statistical analysis of the social tension factors in Russia
Economics and mathematical methods
, 2016, 52 45-66.
The behavior of the mass of the Russian population in the form of protest movements is discussed and analyzed. The hypothesis of political causation for the protests by terms of socio-economic life isn’t rejected. The empirical basis of the study are the data on protest activity of the population in 2011–2012 years, formed on the basis of printed and electronic federal and regional media as well as the content of social networking in Internet. It ñîntains mathematical and statistical analysis of various forms of public discontent and protests of various kinds. Two integral indexes are obtained from the principal component analysis: the index of social tension, which accumulates all kinds of protests, and index of social dissatisfaction, and which reflects all forms of discontent. The numerical values of these indices allow a comparison and ranking of different regions of Russia on the socio-political and economic environment. There is a statistically significant linear relationship shown between the two indices. The found regression makes it possible to carry out a conditional forecast of changes in social tension with changing certain indicators of social and economic discontent of the population.
Keywords: regions, protest movements, protests, social tensions, social discontent, the quality of living, the principal component analysis, regression analysis, conditional forecast.
JEL Classification: C43.

Smolyak S.A. (Moscow) About the problem of early termination of the investment project
Economics and mathematical methods
, 2016, 52 (1), 67-78.
We consider investment projects in the real sector of economy with several participants. There may be situations where some participant may find its advantages to terminate their participation in the project. This leads to organizational difficulties and often – to the termination of the project. To guard against such situations, it is important to provide in advance with organizational and economic assurance tools of project realization. We propose an assessment criterion that would help reveal the possibility of occurrence of such situations. It may be interpreted as a modified IRR.
Keywords: project, investor, NPV, rate of return, project continuation, project termination, optimization.
JEL Classification: C52, D21, D46, G31, O22.

Andreeva A.V., Bogdanova T.K. (Moscow) Predicting the size of the company-customer base based on the Markov chains
Economics and mathematical methods
, 2016, 52 (1), 79-94.
The article represents the information and logical complex model to manage the company’s customer base in order to calculate the index of long-term value of the client. In contrast to the previous issues this model takes into account the peculiarities of consumer behavior and socio–demographic characteristics of the client groups, and the movement of customers within the customer base is represented as a Markov chain. Developed complex dynamic model to manage the company’s customer base makes possible to forecast the cluster frequency and the client base at all on any period, to analyze the population- change-dynamics of client cluster and to highlight the most important stages in the formation and development of the customer base. On each stage highlighted groups of clients are estimated according to future company’s profit and potential for cross selling of products/services. The estimates allow to calculate the budget for marketing activities on retention of given profit level and to compose the most effective plan of address–directed marketing activities.
Keywords: management of customer base of the company; retail trade; group of clients; customer loyalty; buying behavior; Markov chain; dynamic model; long-term value of the customer base.
JEL Classification: C15, C32, C53

Borodin K.G. (Moscow) Forecasting model of the commodity markets development in the conditions of changing state policy
Economics and mathematical methods
, 2016, 52 (1), 95-111.
The forecasting model of development of the commodity market is presented, allowing, in a scenario mode to change value of the import duty and investments into production, and thus to achieve in the long term optimum states for indicators of demand, supply and the price in the domestic market. In model the effects of import duty and investments on key parameters of the commodity market are considered. Some practical possibilities of the model are shown on the example of the meat market (beef, pork and poultry meat markets). Optimization problems are solved by calculating the value of import duty and the investment required: to double domestic production of beef, for maximum ratio between the volume of domestic pork production and imports, to assess the value of investments, allowing to keep production at the same level while reducing the import duty on poultry to 20%.
Keywords: commodity market, import duty, investments, development forecast.
JEL Classification: Ñ510, Ñ530, Ñ540.

Suslov V.I., Domozhirov D.A., Ibragimov N.M., Kostin V.S., Melnikova L.V., Tsyplakov A.A. (Novosibirsk) Agent-based multiregional input-output model of the Russian economy
Economics and mathematical methods
, 2016, 52 (1), 112-131.
The paper for the first time presents a concept and a pilot version of an agent-based multiregional input-output model (ABMIOM) of the Russian economy. In this model independent economic agents interact in the space in the conditions of bounded information, which corresponds to the modern out-of-equilibrium paradigm of economic modeling. The model presented differs of some existing agent-based models as follows: 1) it presents the whole economy rather than a specific segment of the market; 2) it takes in account the geographic locations of agents explicitly; 3) it is compatible with an existing normative model (multiregional input-output model) and is based on real data. Special attention is paid to the evolution of the equilibrium concept in the modeling of economic systems, especially, of spatial economies, to the algorithm of the search of equilibrium and to possibilities of studying it. Some presented results of experimental calculations allow to analyze the convergence of the model to the state of quasi-equilibrium.
Keywords: agent-based models, interaction of agents, economic space, equilibrium.
JEL Classification: C63, R1, D58.

Lesik I.A., Perevozchikov A.G. (Moscow) Determination of the optimal production volumes and sales prices in the linear model of multiproduct monopoly
Economics and mathematical methods
, 2016, 52 (1), 132-140.
An algorithm of determining the volume of production and sales prices, maximizing firm profit in a multiproduct manufacturing and general resource limits is proposed. This article is based on the ideas of (Mishenko and Artyomenko, 2012). The main peculiarity of the model dis-cussed in the article is the assumption that in addition to the production volumes it enables to set the product selling price. As in the Mishchenko-Artyomenko model, the case planning for one period is analyzed. It is proved that the decision of the primary problem of optimizing Pareto non-dominant process and output volumes can be reduced to the problem of quadratic program-ming. It allows to find an alternative function of annual income for monopolies for the dynamic model of investment described in (Perevozchikov, Lesik, 2014). A model of monopoly from (Vasin, Morozov, 2005) for multiproduct market is analyzed in the article. A function of supply and Walras equilibrium is proposed for the purpose. Proved the theorem of existence and uniqueness of balanced and monopolistic prices, Pareto non-dominated. Obtained geometrical balanced and monopolistic prices providing the difference between monopolistic and balanced prices.
Keywords: multiproduct monopoly model, production volume, sales prices, general limitations on resources, the optimal strategy.
JEL Classification: O12, C51.


Vol. 52, No. 2

Glaziev S.Yu. (Moscow) National economy structures in the global economic development
Economics and mathematical methods
, 2016, 52 (2), 3-29.
The author discusses the fundamental issues of long-term economic development, representing a sequential process of change in technology and global economic modes. The patterns of substitution of technological modes and the long waves of the economic conjuncture connected with them have been disclosed in the earlier works of the author, the concept of the global economic mode as a whole system of institutions, providing the economic reproduction, is introduced for the first time. The life cycles of the four global economic modes and their connection with world wars have been traced. Inevitability of transition to a new global economic mode and move of the center of the world economy from the USA to South East Asia has been validated; the threats of a new world war for global domination have been assessed. The author showed that due to this process the U.S. aggression is aimed in the post- Soviet space, at tightening control over its financial and economic periphery in order to strengthen their advantages in competition with China. Proposals for the development strategy and economic policy of Russia to neutralize the risks of defeat and integration into the core of a new global economic mode have been validated.
Keywords: the cycle of capital accumulation, technological structure, world economic structure, technological collection.
JEL Classification: O1, O20, O33, P21, F02, F62, N10.
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Nikonov V. (2015. Present World and its Sources. Moscow: Izdatel'stvo MGU (in Russian).
Perez C. (2002). Technological Revolutions and Financial Capital: The Dynamics of Bubbles and Golden Ages. L.: Elgar.
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Nizamutdinov M.M., Oreshnikov V.V. (Ufa) Formation of the target indicators of regional development strategy using fuzzy logic algorithms
Economics and mathematical methods
, 2016, 52 (2), 30-39.
The article deals with the strategy of regional development on the basis tools of economic-mathematical modeling of social and economic systems. Preliminary analysis of approaches and software solutions in this sphere showed that in the first instance the aspects of definition of the quantitative characteristics require consideration of the purposes of development and elaboration of regulatory impact for their achievement. The approach to formation of the indicative plan and parameters of control within justification of medium-term strategy of regional development, integrating procedures of the goal-setting and regulation, characterized by the existence of indistinct algorithm of classification of situations and corrections the values of parameters of management in the conditions of mutual adaptation of interests of the various subsystems of the region. Criteria of assessment of the situation, function of accessory and base of indistinct rules were developed for use of methods of fuzzy logic. Besides, created the complex of adjustment rules of the control parameters. The proposed approach allows to associate a model of functioning of the economic agents with a model definition of the objectives of regional development into a unified system of feedback control, and ensure the most efficient use of resources at the formation of the medium-term strategy of regional development.
Keywords: regional development strategy, indicative plan, modeling, fuzzy logic.
JEL Classification: Ñ69.
REFERENCES (with English translation or transliteration)
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Il'yasov B.G., Degtyareva I.V., Makarova E.A., Valitov R.R. (2012). The System of Intellectual Support of Decision Making in the Management of Macro-Economic Reproduction Process on the Basis of Simulation. Vestnik UGATU 3, 217-229 (in Russian).
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Nizamutdinov M.M. (2009). Simulation Modeling as a Tool to Justify the Medium-Term Regional Development Strategies. Economics and Management: Research and Practice Journal 5, 104-110 (in Russian).
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Ilinskiy D.G. (Moscow) Lines of savings and loan tariff plans: properties
Economics and mathematical methods
, 2016, 52 (2), 40-59.
In article Ilinskiy, Polterovich, Starkov (2014à) we investigate the transition from the saving and loan programs of mortrage to modern institutes. The concept of LSTP (Lines of Savings and Loan Tariff Plans) was introduced. The parameters of LSTP are realizing the "smooth" changing from subsidizing plans to commercial. The following properties were observed: fairness, fullness, rightness, local rightness, effectiveness. In this paper we analyse connections between this properties for wide class of LSTP. We find the profit of agents using the LSTP in terms of parameters. We prove, that the concepts rightness and local rightness are equivalent. We show that effective LSTP can be changed by effective fairness LSTP with same profit of agents. The conditions on effective LSTP to be full are found. Results show that we can simplify the finding of effective (Pareto-optimal) LSTP.
Keywords: mortgage, line of savings and loan plans.
JEL Classification: D02, D14, G21.
REFERENCES (with English translation or transliteration)
Il'inskiy D.G., Polterovich V.M., Starkov O.Yu. (2014b). Designing and Analyzing the Programs of Contractual Savings for Housing: à Dynamic Model. Ekonomika i matematicheskie metody 50, 2, 35-58.
Il'inskiy D.G., Polterovich V.M., Starkov O.Yu. (2014à). Lines of Savings and Loan Tariff Plans: a Generalization of the Bausparkasse Concept. Ekonomika i matematicheskie metody 50, 4, 71-89.
Laux H. (2005). Die buasparfinanzierung. Die finanziellen aspekte des bausparvertrages als spar- und kreditinstrument. 7 Auflage. Frankfurt am Main: Verlag Recht and Wirtschaft GmbH.
Nakopitelnaja ipoteka (2015). Ipotechnoe agenstvo Yugry. Available at: (accessed: July 2015, in Russian). Obzor zhilischnix programm v Obninske (2015). Nedvizhimost' Kaluzhskoy oblasti. Available at: (accessed: July 2015, in Russian).
Plaut P.O., Plaut S.E. (2004). The Economics of Housing Saving Plans. The Journal of Real Estate Finance and Economics, 28, 4, 319-337.
Polterovich V.M., Starkov O.Yu. (2007). Creating Mortgage Markets for a Catching up Economy: a Problem of Institutional Transplantation. Moscow: Nauka.
Polterovich V.M., Starkov O.Yu. (2010). Poetapnoe formirovanie massovoi ipoteki i rinka zhilja. In: "Strategy of Modernization of the Russian Economy". Polterovich V.M. (ed.). SPb.: Aleteya.
Polterovich V.M., Starkov O.Yu. (2011). Proektirovanie vihoda iz institutsionaljnoi lovushki (na primere ipoteki v Rossii). Available at: task=view id=1839 Itemid=270 (accessed: July 2015, in Russian).
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Svetlov N.M. (Moscow) Econometric analysis of expansion of surface transportation networks
Economics and mathematical methods
, 2016, 52 (2), 60-74.
A disequilibrium theoretical model of long-term economic dynamics, which considers availability of an aggregated resource and satisfaction of needs in specific outputs, is tested against the expansion of surface transportation networks. The 1871-2013 time series of the length of the USA railroads, highways, pawed roads, surfaced roads and total automobile roads, some of which lack numerous observations, are used for the empirical testing. Two incomplete non-linear auto-regression empirical specifications are applied, which differ in the lag duration (one year and 13 years). The both are estimated using generalized maximum entropy (GME) procedure, which is enriched with the endogenous supporting values for the parameter estimates. For the purpose of testing null hypotheses a non-parametric criterion of statistical indiscriminability of two series (reference and compared) is developed, using an area of intersect of polygons of empirical distributions as a critical value. The empirical specification assuming one year lag supports the proposed theoretical model. The parameter estimates do not support the influence of Schumpeterian technological structure changes on the extension of the transportation networks. The possible reason is the fixed correspondence between a given type of the network and a certain technical structure, which is assumed by the empirical specification. The specification with the 13 year lag is rejected, thus giving no evidence for the significance of the investment lag for the transportation network expansion processes.
Keywords: surface transportation networks, disequilibrium model, GME, technological structure, investment lag.
JEL Classification: C320, E370, R410.
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Voronovitsky M.M. (Moscow) The dynamic model of the closed market with one commodity and finite linear automata as participants
Economics and mathematical methods
, 2016, 52 (2), 75-90.
The dynamic model of a closed market with one commodity, which is a combination of autonomous and interacting participants, is investigated in the paper. Closure of the market means that quantity of the commodity and amount of money on the market are constant at all the moments of time. Each partner in the market can be in one of the three statuses: à buyer, a seller and not a participant in trade at this moment of time. The interaction is carried out through trade. Partners in the market change their statuses and prices, using the personal information of each of them about trade in the previous moment of time only and trying to secure their partnership in trade at the next moment. The finite automata models the choice of risk degree in definition of new prices. So we study the closed market with one commodity as a system of interacting finite automata. We showed by the computer investigation the convergence of the average price of the market to a neighborhood of some his average value. We also investigated the role of volume of automata's memory, which represent the participants of market, on the behavior of all our system.
Keywords: mathematical model, closed market, one commodity market, dynamics of prices, trajectory, stationary set, stationary state, finite automata.
JEL Classification: C51, D01.
REFERENCES (with English translation or transliteration)
LeBaron B., Brian W.A., Palmer R. (1999). Time Series Properties of an Artificial Stock Market Model. Journal of Economic Dynamics and Control 23, 1487-1516.
Makarov V.L. (2012). Artificial Societies. Economics and Mathematical Methods 48, 3, 3-20 (in Russian).
Topol R. (1991). Bubbles and Volatility of Stock Prices; Effect of Mimetic Contagion. The Economic Journal, 101, 786-809.
Tsetlin M.L. (1969). Automaton Theory and Modeling of Biological Systems. Moscow: Nauka (in Russian).
Voronovitsky M.M. (1974). One Model of Exchang. Automatika i Telemekhanika 8, 85-92 (in Russian).
Voronovitsky M.M. (2014). The Agent-Based Model of the Closed Market with One Commodity. Ekonomika i matematicheskie metody, 50, 2, 58-72 (in Russian).
Voronovitsky M.M. (2015). The Agent-Based Model of the Closed Market with One Commodity and Rational Choice of Partners. Economics and Mathematical Methods 51, 3, 75-91 (in Russian).

Matveenko V.D., Bronshtein Ye.M. (St-Petersburg, Ufa) On the properties of CES production functions in a model of production with intermediate goods
Economics and mathematical methods
, 2016, 52 (2), 91-102.
CES production functions are widely used in economic growth and development researches. However, it is not always taken into account that properties of different specifications of CES functions (continual or discrete, with the weights or without them) are rather differ. The properties of CES production functions, essential for analysis of economic models, are studied. The CES function is proved with a finite number of arguments with normalized weights increases with the elasticity of substitution parameter, while under the absence of weights this parameter of the CES function decreases. Pattern of behavior of the CES function with argument x(i), defined on a continual set [0,N], is operated by the value N. Under N = 1 the function with continual argument behaves (in respect of the elasticity of substitution) similarly to the function with a finite number of arguments with weights, but under N > 1 its behavior is quite different. There are important differences between the continual and the discrete CES functions when the elasticity of substitution parameter converges to zero. We show the mistakes when continual CES functions are applied to models of production with intermediate goods which have gained popularity in recent years. We also show some shortcomings of continual models with intermediate goods when using these models for the analysis of economic development problems.
Keywords: production function, CES function, continuous and discrete economical models, monotony, minimum, essential infimum.
JEL Classification: D240.
REFERENCES (with English translation or transliteration)
Afanasyev A.A., Ponomareva O.S. (2014). The Aggregate Production Function of Russian Economy in 1990-2012. Economics and Mathematical Methods 50, 4, 21-33 (in Russian).
Barkalov N.B. (1981). Production Functions in the Models of Economic Growth. Moscow: Izdatel'stvo MGU (in Russian).
Bullen P.S. (2004). Handbook of Means and Their Inequalities. Dordrecht: Kluwer Academic Publishers.
Combes P.-P., Mayer T., Thisse J.-F. (2008). Economic Geography: The Integration of Regions and Nations. Princeton: Princeton University Press.
Dixit A.K., Stiglitz J.E. (1977). Monopolistic Competition and Optimum Product diversity. American Economic Review 67, 3, 297-308.
Dixit A.K., Stiglitz J.E. (2004). Monopolistic Competition and Optimum Product Diversity (May 1974). In: "Monopolistic competition revolution in retrospect" Brakman S., Hejdra B.J. (eds.). Princeton: Princeton University Press, 70-88.
Ershov E.B. (2013). Composite Production Functions. The HSE Economic Journal 17, 1, 108-129 (in Russian).
Ethier W.I. (1982). National and International Returns to Scale in the Modern Theory of International Trade. American Economic Review 72, 3, 389-405.
Growiec J. (2008). Production Functions and Distributions of unit Factor Productivities: Uncovering the Link. Economic Letters 101, 1, 87-90.
Hardy G.H., Littlewood J.E., P?lya G. (1934). Inequalities. Cambridge: Cambridge University Press.
Jones C.I. (2005). The Shape of Production Function and the Direction of Technical Change. Quarterly Journal of Economics 120, 2, 517-549.
Jones C.I. (2011). Intermediate Goods and Weak Links in the Theory of Economic Development. American Economic Journal: Macroeconomics 3, 1-28.
Kleyner G.B. (1986). Production Functions: Theory, Methods, and Application. Moscow: Finansy i statistika (in Russian).
La Grandville O. de (2011). A New Property of General Means of Order p with an Application to the Theory of Economic Growth. Australian Journal of Mathematical Analysis and Applications 8, 1. Article 4.
La Grandville O. de, Solow R.M. (2006). A Conjecture on General Means. Journal of Inequalities in Pure and Applied Mathematics 7, 1, 1-3.
Matveenko A.V., Polyakova E.V. (2012). Modeling of Technological Changes and Changes of Consumer's Preferences. Vestnik of Nekrasov Kostroma State University 18, 6, 159-162 (in Russian).
Matveenko V.D. (2009). An "Anatomy" of Production Functions: a Technological Menu and a Choice of the Best Technology. Economics and Mathematical Methods 46, 2, 105-115 (in Russian).
Nam P.T., Minh M.N. (2008). Proof for a Conjecture on General Means. Journal of Inequalities in Pure and Applied Mathematics 9, 3. Article 86.
Romer P. (1990). Endogenous Technological Change. Journal of Political Economy 98, 5, S71-S102.
Rosen S. (1981). The Economy of Superstars. American Economic Review 71, 5, 845-858.
Solow R. (1956). A Contribution to the Theory of Economic Growth. Quarterly Journal of Economics 70, 1, 65-94.

Kurochkin S.V. (Moscow) The convexity of option prices as a criterion of no-arbitrage
Economics and mathematical methods
, 2016, 52 (2), 103-111.
It is necessary at any time for the market prices to satisfy certain conditions of a set of options with different strike prices on the same reference asset be arbitrage-free. Some conditions of this kind are the consequences of arbitrage-free requirement: monotonicity, Lipschitz-parameters and conxexity. We give the complete set of independent and verifiable convexity-type properties for option prices that are equivalent to the absence of arbitrage. A special version of Farkas lemma was used in the proof of the main result. This construction may be generalized to the dirivatives depending on several reference assets and/or with arbitrary piecewise linear payoff diagrams. It is proved that one may choose a finite set of functions on an option portfolio sufficient to verify the arbitrage-free requirement for this context.
Keywords: option, no-arbitrage pricing, convexity.
JEL Classification: G13.
REFERENCES (with English translation or transliteration)
Bain A. (2011). Arbitrage-Free Option Pricing by Convex Optimization. Available at: (accessed: July 2015).
Bassett G. (1997). Nonparametric Bounds for the Probability of Future Prices Based on Option Values. IMS Lecture Notes-Monograph Series 31, 287-300.
Berg M. de, Cheong O., Kreveld M., Overmars M. (2008). Computational Geometry. Algorithms and Applications. Berlin, Heidelberg: Springer-Verlag.
Cox J., Rubinstein M. (1985). Options Markets. N.Y.: Prentice Hall.
Dmitruk A.V. (2012). Convex Analysis. Moscow: Maks-Press (in Russian).
Fengler M. (2009). Arbitrage-Free Smoothing of the Implied Volatility Surface. Quantitative Finance 9, 4, 417-428.
F?llmer H., Shied A. (2008). Stochastic Finance: An Introduction in Discrete Time. Moscow: MTsNMO (in Russian).
Galitz L. (1998). Financial Engineering. Moscow: TVP (in Russian).
Hull J. (2014). Options, Futures and Other Derivatives. Moscow: Vil'yams (in Russian).
Jeyakumar V. (2009). Farkas Lemma: Generalizations. In: "Encyclopedia of Optimization". Floudas C., Pardalos P. (eds.). Berlin, Heidelberg: Springer-Verlag, 998-1001.
Karatzas I., Kou S. G. (1996). On the Pricing of Contingent Claims under Constraints. The Annals of Applied Probability 6, 2, 321-369.
Kijima M. (2002). Monotonicity and Convexity of Option Price Revisited. Mathematical Finance 12, 4, 411-425.
King A., Koivu M., Pennanen T. (2005). Calibrated Option Bounds. International Journal of Theoretical and Applied Finance 8, 2, 141-159.
Kurochkin S.V. (2005). Payoff Functions Implementable by Option Strategies Ekonomika i matematicheskie metody 41, 3, 135-137 (in Russian).
Kurochkin S.V. (2014). If They Go Away. What will Russian Stock Market without Nonresidents? Rynok tsennykh bumag 8, 57-59 (in Russian).
Lyuu Yu.-D. (2010). Financial Engineering and Computation. Moscow: Binom (in Russian).
Merton R. (1973). Theory of Rational Option Pricing. The Bell Journal of Economics and Management Science 4, 1, 141-183.
Moscow Exchange (2015). Official Site. Derivatives Market. Available at: (accessed: July 2015, in Russian).
Panjer H. (2005). Financial Economics. Moscow: Yanus-K (in Russian).
Perrakis S., Ryan P. (1984). Option Pricing Bounds in Discrete Time. The Journal of Finance 39, 2, 519-525.
Rokafellar R. (1973). Convex Analysis. Moscow: Mir (in Russian).
Roos K. (2009). Farkas Lemma. In: "Encyclopedia of Optimization". Floudas C., Pardalos P. (eds.). Berlin, Heidelberg: Springer-Verlag, 995-998.
Wang Y., Yin H., Qi L. (2004) No-Arbitrage Interpolation of the Option Price Function and Its Reformulation. Journal o Optimization Theory and Applications 120, 3, 627-649.

Grebnev M.I., Shults D.N. (Perm) Statistical method of production functions aggregation
Economics and mathematical methods
, 2016, 52 (2), 112-128.
The article discusses the aggregation of production functions (PF). It is shown that consistent aggregation of PF is possible only in very special cases. A statistical aggregation method is suggested. It allows to synthesize new kinds of macroeconomic PF. Macroeconomic PF for the US economy based on industrial Cobb-Douglas PF with a normal distribution parameters is constructed and investigated. For the Russian economy the aggregate PF obtained on the basis of sectoral and regional Cobb-Douglas PF. It is shown that in case of scarcity of statistical data the more correct estimations of the aggregate PF for Russia may be derived using regional PF.
Keywords: production function, consistent aggregation, statistical approach.
JEL Classification: C43; D24; E23.
REFERENCES (with English translation or transliteration)
Bessonov V.A., Tsukhlo S.V. (2002). The Analysis of Russian Transition Economy Dynamics. Moscow: Institute for Transition Economy (in Russian).
Dresch F.W. (1938). Index Numbers and the General Economic Equilibrium. Bulletin of the American Mathematical Society 44, 134-141.
Ershov E.B. (2013). Composite Production Functions. The HSE Economic Journal 17, 1, 108-129 (in Russian).
Felipe J., Fisher F.M. (2003). Aggregation in Production Functions: What Applied Economists Should Know. Metroeconomica 54, 3, 208-262.
Felipe J., McCombie J.S.L. (2013). The Aggregate Production Function and the Measurement of Technical Change: "Not Even Wrong". Cheltenham: Edward Elgar.
Fel's E., Tinter G. (1971). Methods of Economic Research. Moscow: Progress (in Russian).
Grebnev M.I. (2013). Construction Aggregate Production Function for the Economy of Russia. European Social Science Journal 1, 12, 438-445 (in Russian).
Klein L.R. (1946a). Macroeconomics and the Theory of Rational Behavior. Econometrica 14, 2, 93-108.
Klein L.R. (1946b). Remarks on the Theory of Aggregation. Econometrica 14, 4, 303-312.
Kleyner G.B. (1986). Production Functions: Theory, Methods, Applications. Moscow: Finance and Statistics (in Russian).
Koen A., Kharkurt Dzh. (2009). Whatever Happened to the Cambridge Capital Theory Controversies? Voprosy Economiki 8, 4-27 (in Russian).
Leontief W.W. (1947). Introduction to a Theory of the Internal Structure of Functional Relationships. Econometrica 15(4), 361-373.
May K. (1946a). The Aggregation Problem for a One-Industry Model. Econometrica 14, 4, 285-298.
May K. (1946b). Technological Change and Aggregation. Econometrica 15, 1, 51-63.
Perskij Yu.K., Shultz D.N. (2005). Government Regulation of Economy as Hierarchical System. Journal of Economic Theory 2, 25-46 (in Russian).
Petrov A.A., Pospelov I.G., Shananin A.A. (1996). The Experience in Mathematical Modeling of Economy. Moscow: Energoatomizdat (in Russian).
Porokhovskiy A.A. (2002). The Vector of Economic Development. Moscow: TEIS (in Russian).
Pospelov I.G. (2001). Economic Agents and Systems of Balances. Preprint WP2/2001/03. Moscow: National Research University Higher School of Economics (in Russian).
Pu S.S. (1946). A Note on Macroeconomics. Econometrica 14, 4, 299-302.
Shul'ts D.N. (2014a). Microeconomic Funding of Macroeconomics and the Bohr's Principle of the Complementarity. Vestnik Instituta ekonomiki Rossijskoj akademii nauk 2, 157-165 (in Russian).
Shul'ts D.N. (2014á). Hierarchical Analysis of Economy in Economics Mainstream of the 20th Century. Journal of Economic Theory. ¹ 2. Ñ.130-138 (in Russian).

Nevecherya A.P. (Krasnodar) Analysis of labor force dynamics in intersectoral mathematical model of the labor market
Economics and mathematical methods
, 2016, 52 (2), 129-140.
We propose mathematical model of self-organization of the labor force. This model is based on the balance equations for the number of employed and unemployed in different sectors of economy. The unemployed are divided by their last place of employment. The mathematical model was transformed to a more convenient form for numerical analysis. The tasks of analyzing the dynamics of the labor force and forecasting of the number of employed and unemployed were set for the model. Methods for estimation of the exogenous variables of the model were proposed. Theoretical results were applied for solving the specific problems. In the above examples was used the real data of the number of employed and unemployed at the labor market of the Russian Federation for 2011-2013 years. The Federal State Statistics Service provides this information. The forecast of the labor force by the economy sectors for 2013 was made on the data for 2011 and 2012 years. The calculated data was compared with statistical data for the same 2013 year. It was shown that the error of the forecast of the number of employed by the economy sectors of the Russian Federation does not exceed 2%. We concluded that the proposed model is adequate.
Keywords: labor market, self-organization, dynamics of the labor force, forecast, vector presentation of the model.
JEL Classification: C390.
REFERENCES (with English translation or transliteration)
Berezhnaya E.V., Berezhnoy V.I. (2006). Mathematical Methods of Modeling Economic Systems. Moscow: Finansy i statistika (in Russian).
Federal State Statistics Service (2015). Labor Force. Available at: wps/wcm/connect/rosstat_main/rosstat/ru/statistics/wages/labour_force (accessed: July 2015, in Russian).
Gimpel'son V.E., Kapelyushnikov R.I., Ryzhikova Z.A. (2012). The Movement of Workplaces in the Russian Economy: in Search of Creative Destruction. Preprint. Moscow: Preprandially the house of the Higher school of Economics (in Russian).
Semenchin E.A., Nevecherya A.P. (2014). The Inverse Problem in the Mathematical Model of Self-Organization of the Labor Market. Fundamental research 6, 1184-1190.
Semenchin E.A., Zaytseva I.V. (2007). The Mathematical Model of Self-Organization of a Labor-Market for a Number of Branches of Economy. Ekonomika i matematicheskie metody 43, 1, 133-136 (in Russian).
Tikhonov A.N., Arsenin V.Ya. (1979). Methods for Solving Incorrectly Posed Problems. Moscow: Nauka (in Russian).


Vol. 52, No. 3

Glaz'ev S.Yu. (Moscow) Applied results in the theory of world economic structures
Economics and mathematical methods
, 2016, 52 (3), 3-21.
The article presents the results of the applied research of the ongoing changes in the global economic and political system, made on the basis of the theory of world economic structures. This theory of the issue is described in the article in the previous issue of the journal. These changes are due to the processes of change in technology and world economic structures. As in previous long cycles, this transition is accompanied by exacerbation of international political tensions associated with the desire of the dominant country to maintain leadership by unleashing world war in order to retain control over the periphery of its financial and economic system. These objective circumstances explain the aggressive policy of the U.S. seeking to strengthen their opportunities. To do that the USA wage a hybrid war in the peripheral regions of the global economic system. This article proves the inevitability of the movement of the centre of the world economy to Asia, and reveals the risks of world war and the threat to Russia connected with them. Measures to prevent these risks and threats, including the formation of institutions of the new world economic order and implementation of the strategy of outstripping development of Russia based on the growth of new technological order, are justified.
Keywords: world economic structure, the cycle of capital accumulation, long waves, technological structures, world wars, development strategy, anti-war coalition.
JEL Classification: O11, O20, O33, P21, F02, F62, N10.
REFERENCES (with English translation or transliteration)
Ajvazov A. (2012). Periodic System of the World Capitalism. Author's site. (in Russian).
Ershov M. (2015). Financial Crisis: Possibility is Becoming Obvious. Expert 36, 12 (in Russian).
Filimonov G. (2012). Cultural and Information Mechanisms of USA Foreign Policy. The Sources and the New Reality. Moscow: Rossijskij universitet druzhby narodov (in Russian).
Glaz'ev S. (1993). Theory of Long-Term Technical and Economic Development. Moscow: VlaDar (in Russian).
Glaz'ev S. (2013). About the International Initiative for G20 for Developing the Systems of Protecting the Earth from the Space Threats. Analytical report. Available at: (in Russian).
Huntington S.P. (1996). The Clash of Civilizations and the Remaking of World Order. N.Y.: Simon and Schus
ter. K'eza D. (2014). What is Instead of Catastrophe. Moscow: ID "Tribuna" (in Russian).
Koncepciya uchastiya Rossii v ob"edinenii BRIKS (2013). Utverzhdena Prezidentom V. Putinym 21 marta 2013 g. (in Russian).
Pantin V. (2014). The Most Possible Prognosis of Development of the Political and Military Conflicts in 2014-2018. Analytical report. 12 July. Available at: (accessed: February 2016, in Russian).
Perspectives and Strategic Priorities of BRIC Development (2014). V. Sadovnichego, Yu. Yakovca, A. Akaeva (eds.). M.: MGU, Mezhdunarodnyj institut Pitirima Sorokina-Nikolaya Kondrat'eva, INE'S, Nacional'nyj komitet po issledovaniyu BRIKS, Institut Latinskoj Ameriki RAN (in Russian).
Rogov S. (2012). Russia in the Multi-Polar World. A report. Moscow: Institut SShA i Kanady RAN (in Russian). Available at: (accessed: March 2016, in Russian).
Toloraya G. (2014). BRIC and the New Economic Order. In: "Prospects and strategic priorities of BRIC development" V. Sadovnichego, Yu. Yakovca, A. Akaeva (eds.). M.: MGU, Mezhdunarodnyj institut Pitirima Sorokina-Nikolaya Kondrat'eva, INE'S, Nacional'nyj komitet po issledovaniyu BRIKS, Institut Latinskoj Ameriki RAN (in Russian).

Pinskaya M.R., Kolesnik G.V. (Moscow) The differentiation of the authority in tax incentives among the federal and regional levels. Fiscal implications
Economics and mathematical methods
, 2016, 52 (3), 22-35.
The authors study the problems of differentiation in the authority levels to establish tax incentives among the federal and regional government bodies and assess the corresponding negative impact on the tax competition. It is shown that the federal intervention in the regional tax privileges may lead to a distortion of vertical tax competition, a shortfall in tax revenues in the regional budgets, as well as to the migration of the tax base between regions, thereby distorting the real picture of the profits allocation. The obtained results can be used by federal and regional public authorities for developing the proposals to improve mechanisms of tax privileges provision and interbudgetary transfers' optimization.
Keywords: tax powers, tax privileges, tax competition, profit tax, property tax, regional budget, interbudgetary relations, federative system, vertical tax effect, consolidated group of taxpayers.
JEL Classification: H23, H32, H71.
REFERENCES (with English translation or transliteration)
Auerbach A., Summers L.H. (1979). The Investment Tax Credit: An Evaluation. NBER Working Paper Series. No. 404.
Bykov S.S. (2013). Classification of Tax Privileges As a Condition and a Stage of Their Effectiveness Evaluation. Izvestiya of Irkutsk State Economics Academy 5, 20-26 (in Russian).
Fleming J.C., Peroni R.J. (2010). Can Tax Expenditure Analysis Be Divorced from a Normative Tax Base: A Critique of the 'New Paradigm' and its Denouement. Virginia Tax Review 30, 135-180.
Keen M., Kotsogiannis C. (2002). Does Federalism Lead to Excessively High Taxes? American Economic Review 92, 1, 363-370.
K?thenb?rger M. (2002). Tax Competition and Fiscal Equalization. International Tax and Public Finance 9, 4, 391-408.
Kraan D.-J. (2004). Off-Budget and Tax Expenditures. OECD Journal on Budgeting 4, 1, 121-142.
Mayburov I.A., Ivanov J.B. (2014). Tax Benefits. The Theory and Practice of Application. Moscow: Unity-Dana (in Russian).
McIntyre M.J. (1980). A Solution to the Problem of Defining a Tax Expenditure. U.C. Davis Law Review 14, 1, 83-89.
Nalogovye l'goty: analiz praktiki primeneniya i metodika otsenki effektivnosti deystviya. (2011). Rekomendatsii soveshchaniya Komiteta Soveta Federatsii po byudzhetu 14 aprelya 2011 goda. Available at: (accessed: November 2015, in Russian).
Savina O.N. (2013). Evaluation of the Effectiveness of Tax Incentives in the Modern Practice of Taxation and the Ways of Its Improvement. Taxes and taxation 8(110), 579-598 (in Russian).
Shick A. (2007). Off-Budget Expenditure: An Economic and Political Framework. OECD Journal on Budgeting 7, 3, 1-32.
Sozdanie konsolidirovannykh grupp nalogoplatel'shchikov otritsatel'no povliyalo na postuplenie naloga na pribyl' v byudzhetnuyu sistemu Rossiyskoy Federatsii (2014). Schetnaya palata RF. Rezul'taty ekspertno-analiticheskogo meropriyatiya Schetnoy Palaty RF. Available at: (accessed: November 2015, in Russian).
Surrey S. (1976). The Tax Expenditure Concept and the Budget Reform Act of 1974. Boston College Law Review 17, 5, 679-737.
Tatarkin D.A., Sidorova E.N. (2010). Tax Federalism in the Incentive System of Regional Self-Development. Taxes and Financial Law 4, 339-342 (in Russian).
Toder E. (2005). Tax Expenditures and Tax Reform: Issues and Analysis. In: "Proceedings of National Tax Association Meetings". November 19. Miami.
Toder E., Wasow B., Ettlinger P.M. (2002). In Bad Breaks All Around: The Report of the Century Foundation Working Group on Tax Expenditures. N.Y.: The Century Foundation Press.
Villela L., Lemgruber M., Jorratt M. (2010). Tax Expenditure Budgets. Concepts and Challenges for Implementation. Inter-American Development Bank Working Paper Series. No. IDB-WP-131.
Voloshchuk S.D. (2009). Evaluation of the Effectiveness of Management of Objects of the Military-Industrial Complex on the Basis of Social Value Indicators. Moscow: Nauka (in Russian).
Wilson J.D. (1986). A Theory of Interregional Tax Competition. Journal of Urban Economics 19, 3, 296-315.
Zodrow G., Mieszkowski P. (1986). Pigou, Tiebout, Property Taxation and the Underprovision of Local Public Goods. Journal of Urban Economics 19, 3, 356-370.

Afanasyev D.O., Fedorova E.A. (Moscow) Econometric analysis of mutual influence of Russia and the developed countries
Economics and mathematical methods
, 2016, 52 (3), 36-49.
This study examines issues of the level assessment of monetary, financial, macroeconomic and trade integration between Russia and four developed countries - China, Germany, the United Kingdom and the USA. The changes of integration level in the crisis periods were analyzed, and the presence or absence of spillover-effects in the respective channels of contagion was conclude. The research methodology is vector autoregressive model with Markov regime-switching and the analysis of estimated covariance matrix. The study shows that the spillover-effect is most likely occurs between Russia and United Kingdom (financial, macroeconomic and trade channels), while completely missing with China. For Germany and the United States revealed one channel flow crisis in Russia: trade and finance, respectively.
Keywords: crisis, channels of contagion, spillover-effect, Markov regime-switching model.
JEL Classification: Ñ01, E44, E47.
REFERENCES (with English translation or transliteration)
Fedorova E., Bezruk O. (2011). The Channels of Financial Crisis Transmission in Emerging Markets. Voprosy Economiki 7, 120-128 (in Russian).
Fedorova E.À., Afanasyev D.O. (2014). Comprehensive Crisis Indicator for Russia. Journal of the New Economic Association 3(23), 38-59 (in Russian).
Fedorova E.À., Afanasyev D.O. (2014). Transmission Channels of Crisis Situations in the Russian Federation and their Identification. Studies on Russian Economic Development 5(25), 500-508.
Hamilton J.D. (1989). A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle. Econometric 57, 357-384.
Hamilton J.D., Lin G. (1996). Stock Market Volatility and the Business Cycle. Journal of Applied Econometrics 11, 573-593.
Kuan Ch.-M. (2013). Markov Switching Model. Quantile 11, 13-39. Available at: (accessed: February 2016, in Russian).
Kydland F., Prescott E. (1990). Business Cycles, Real Facts and a Monetary Myth. Federal Reserve Bank of Minneapolis Quarterly Review 14, 3-18.
Masson P. (1998). Contagion: Monsoonal Effects, Spillovers, and Jumps between Multiple Equilibria. IMF Working Paper 98/142.
Masson P. (1999). Contagion: Macroeconomic Models with Multiple Equilibria. Journal of International Money and Finance 18, 587-602.
Perlin M. (2012). MS_Regress The Matlab Package for Markov Regime Switching Models. SSRN. Available at: (accessed: February 2016).
Solntsev O.G., Mamonov M.E., Pestova A.A., Magomedova Z.M. (2011). Experience in Developing Early Warning System for Financial Crises and the Forecast of Russian Banking Sector Dynamics in 2012. Journal of the New Economic Association 12, 41-76 (in Russian).

Melent'ev B.V. (Novosibirsk) Forecasting cash flows based on the inter-regional cross-sectoral models
Economics and mathematical methods
, 2016, 52 (3), 50-64.
The article gives characteristics of inter-regional financial balance "Payments-Income" for calculating the aggregated price indices corresponding to the basic properties of the current prices. Our calculations in comparison with classical cross-sectoral "Input-Output" models without regional factors show the improvement of the tool to quantify the financial ratios associated with different by years material forecasts of regional economic development. Calculated values of financial ratios are balanced across sectors and regions of the country. The difference between them is determined by the accepted policy of regionally differentiated income tax, budgetary support and loans. The use of inter-regional financial balance "Payments-Income" is relatively new and not fully developed because of an extremely large volume of the object. The results of experimental calculations are given for the period until 2025 year for 20 regions of Russia and 53 industries.
Keywords: forecasting of economic development, inter-regional cross-sectoral models, financial proportions.
JEL Classification: C02.
REFERENCES (with English translation or transliteration)
Dmitriev V.K. (1904). Economic Objects. (Reissue: Dmitriev V.K. (2001). Economic Objects. Moscow: MGU; VShE) (in Russian).
Granberg A.G. (1985). Dynamic Modeling of the National Economy. Moscow: Ekonomika (in Russian).
Isard W. (1966). Methods of Regional Analysis: Introduction into the Rationalistic. Moscow: Progress (in Russian).
Kantorovich L.V. (1960). Economic Calculations for the Optimal Use of Resources. Moscow: Izdatel'stvo AN SSSR (in Russian).
Makarov V.L. (1966). Production Linear Dynamic Models. In: "Optimal Planning". Vol. 5. Novosibirsk: Nauka, SO (in Russian).
Melent'ev B.V. (2013). Evaluation of Variants of Economic Regulation with the Help of Interregional "Payments-Income" Tools. Studies on Russian Economic Development 6, 24, 6, 570-577 (in Russian).
Melent'ev B.V., Ershov YU.S., Alimpieva A.A. (2010). Methodological Recommendations for Drawing up a Financial Balance-Sheet of Inter-Regional and Inter-Trade "Expenses-Revenues". Novosibirsk: IEiOPP SO RAN (in Russian).
Prognoz dolgosrochnogo sotsial'no-ekonomicheskogo razvitiya Rossiyskoy Federatsii na period do 2030 goda. (2013). Available at: (accessed: June 2014, in Russian).
Prognoz makropokazateley Rossiyskoy Federatsii (2015). Quarterly Report No. 33. Available at: (accessed: October 2015, in Russian).
Shirov A., Yantovskiy A. (2008). About the Instruments of the Long-Term Macroeconomic Prognostics. The Economist 2, 31-44 (in Russian).
Suslov V.I., Kostin V.S., Zabinyako G.I., Kotel'nikov E.A., Melent'ev B.V. (2011). Model-program complex for prognosis of large financial protocols for branches and regions of the country. Certificate of Program State Registration for ECM No. 2011617654. M.: Federal'naya sluzhba po intellektual'noy sobstvennosti, patentam, 30.09.2011 (in Russian).
Uzyakov M.N. (2003). Methodological Approaches to the Analysis of Regional Economic Development Using a Model "Expenses-Output". In: "Methods of Making Regional Prognosis" Vserossiyskaya nauchno-prakticheskaya konferentsiya. Moscow: RINTs (in Russian).

Orel Ye.N., Orel O.Ye. (Moscow) Optimal production control of order performing by delivery date
Economics and mathematical methods
, 2016, 52 (3), 65-77.
The application peculiarities of optimal control models in economic problems are discussed. Attention is stressed in the need to find the global extremum. To this end it is proposed, as in the calculus of variations, to build central fields of extremals and examine them for global extremum. The central field consists of extremals emanating from the initial point and once covering the reachable area. Since building such a field is analytically much harder than finding one extremal, which may be interpreted only as a local extremum, paying more attention to numerical methods is recomended. This program is being implemented at a known problem that is to perform an order for a production by given time at minimum cost. The central field of Pontryagin's extremals is built. An extremal of general position consists of three stages. First, there is a waiting period, then - the gradual deployment of incremental production rate, and at the last stage - the production at maximum speed. It is proved that the field is smooth, so that each trajectory is optimal in the usual sense. For this model numerical experiments were conducted. The family of trajectories constructed numerically is almost indistinguishable visually from the analytical constructed field of extremals. This emphasizes the closeness and adequacy of both approaches.
Keywords: optimal control, order, production output, global extremum, central field of trajectories.
JEL Classification: C61.
REFERENCES (with English translation or transliteration)
Caputo M.R. (2005). Foundations of Dynamic Economic Analysis: Optimal Control Theory and Applications. Cambridge: Cambridge University Press.
Dowling E.T. (2000). Introduction to Mathematical Economics. Schaum's Outline Series. N.Y.: McGraw Hill.
Fleming U., Rishel R. (1978). Deterministic and Stochastic Optimal Control. Moscow: Mir (in Russian). [Fleming U., Rishel R. (1975). Deterministic and Stochastic Optimal Control. N.Y.: Sspringer-Verlag.]
Kamien N., Schwartz N. (1991). Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management. N.Y.: Elsevier Science Publishing Co.
Orel E.N. (1989). A Method for Numerical Solution of Optimal Control Problems. Proceedings of the USSR Academy of Sciences 306, 1301-1304.
Orel E.N., Orel Î.Å. (2013). Global Extremum in Autonomous Problems of Optimal Control. Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya 3, 60-73 (in Russian). [Orel E.N., Orel Î.Å. (2013). Global Extremum in Autonomous Problems of Optimal Control. Journal of Computer and Systems Sciences International 52, 3, 386-399.]
Orel E.N., Orel Î.Å. (2014). Central Fields of Optimal Trajectories. Proceedings of the USSR Academy of Sciences 457, 4, 402-405. [Orel E.N., Orel Î.Å. (2014). Central Fields of Optimal Trajectories. Doklady Mathematics 90, 2, 651-653.]
Orel Å.Í. (1990). Algorithms for Searching of Quasy-Optimal Control Using a Partition of the State Space. Computational Mathematics and Mathematical Physics 29 (9), 1283-1293 (in Russian).
Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V., Mishchenko E.F. (1969). The Mathematical Theory of Optimal Processes. Moscow: Nauka (in Russian). [Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V., Mishchenko E.F. (1962). The Mathematical Theory of Optimal Processes. N.Y.: Wiley.]
Schattler H., Ledzewicz U. (2012). Geometric Optimal Control: Theory, Methods and Examples. N.Y.: Springer.
Young L. (1974). Lectures on the Calculus of Variations and Optimal Control Theory. Moscow: Mir (in Russian). [Young L. (1969). Lectures on the Calculus of Variations and Optimal Control Theory. London: W.B. Saunders Company.]

Arkin V.I., Slastnikov A.D. (Moscow) Comparative analysis of various principles of the granting tax holidays
Economics and mathematical methods
, 2016, 52 (3), 78-91.
The paper considers the model of investment attraction for a creation of new enterprises in the real sector through the mechanism of tax holidays. In the framework of this model, considering the stochastic dynamics of the profits from the enterprise, we give a comparative analysis of three principles of the granting tax holidays on profit tax: 1) holidays of deterministic (fixed) duration; 2) holidays based on the payback period of initial investment; 3) holidays based on the level of profit. For estimating potential possibilities of tax holidays we use an optimization approach to the specification of tax holidays options. The optimality criterions are expected discounted tax payments from the created enterprise into the consolidated budget. As indices for comparing we use the investment level (which characterizes the time of the investor's entry), the NPV from created enterprise, as well as the expected discounted tax payments from the created enterprise into the federal and regional budgets. The comparison is conducted for three types of tax holidays on profit tax which are really used in Russia: full, partial and regional holidays.
Keywords: investment project, tax holidays, stochastic process of profits, profit tax, expected tax payments into the budget, payback period.
JEL Classification: H21, D81, C61.
REFERENCES (with English translation or transliteration)
Arkin V.I. (2014). Threshold Strategies in Optimal Stopping Problem for One-Dimensional Diffusion Processes. Theory of Probability and its Applications 59, 2, 365-374 (in Russian).
Arkin V.I., Slastnikov A.D. (2007). Theory of Investment Expectations, Investment Incentives, and Tax Reform. Economics and Mathematical Methods [Ekonomika i matematicheskie metody] 43, 2, 76-100 (in Russian).
Arkin V.I., Slastnikov A.D., Arkina S.V. (2004). Stochastic Models of Investment Attraction in Real Sector. The Survey of Applied and Industrial Mathematics 11, 3, 433-457 (in Russian).
Arkin V., Slastnikov A., Shevtsova E. (1999). Tax Incentives for Investment Projects in the Russian Economy. Working Paper 99/03. Moscow: EERC.
Dixit A.K., Pindyck R.S. (1994). Investment under Uncertainty. Princeton: Princeton University Press.
Jou J.-B. (2000). Irreversible Investment Decisions under Uncertainty with Tax Holidays. Public Finance Review 28, 1, 66-81.
McDonald R., Siegel D. (1986). The Value of Waiting to Invest. Quarterly Journal of Economics 101, 707-727.
Mintz J.M. (1990). Corporate Tax Holidays and Investment. The World Bank Economic Review 4, 1, 81-102.
Tax Incentives and Foreign Direct Investment. A Global Survey (2000). ASIT Advisory Studies, 16. UNCTAD. N.Y., Geneva: United Nations.

Skripnik D.V. (Moscow) A Macroeconomic model of the Russian economy
Economics and mathematical methods
, 2016, 52 (3), 92-113.
The macroeconomic model of Russian economy is constructed. The model takes into account the key features of behavioral mechanism, economic policy mechanism, and key structural features of the economy. We model the budget rule mechanism, consider interaction of the Central Bank and budget in a context of monetary and budget reserves accumulation. We include two different monetary policy rules in the model: domestic credit rule and exchange rate rule. The exchange rate submodel describes a Balassa-Samuelson effect and terms of trade effect.The model has high forecast power: model forecast quality is higher than Ministry of Economy Development of Russian Federation forecast quality for majority of macroeconomic indicators.
Keywords: macroeconomic modeling, error correction model, budget rule, transmission mechanism of monetary policy.
JEL Classification: E170, Ñ530, Ñ510.
REFERENCES (with English translation or transliteration)
Aguiar M., Gopinath G. (2007). The Role of Interest Rates and Productivity Shocks in Emerging Market Fluctuations. Central Bank of Chile.
Aivazian S.A. Brodsky B.E. (2006). Macroeconometric Modeling: Modern Trends, Problems, an Example of the Econometric Model of the Russian Economy. Applied Econometrics 2, 85-111 (in Russian).
Alekseev A.V., Sokolov D.V., Turdieva N.V., Yudaeva K.V. (2006) Russia and the International Trading Organizations: the Analysis within the Limits of the General Equilibrium Model. Economics of Contemporary Russia 4, 112-125 (in Russian).
Bardsen G., Eitrhei O., Jensen E., Nymoen R. (2005). The Econometrics of Macroeconomic Modelling. Oxford: Oxford University Press. Basdevant O. (2000). An Econometric Model of the Russian Federation. Economic Modelling 17(2), 305-336.
Benedictow A., Fj?rtoft, L?fsn?s O. (2010). Oil Dependency of the Russian Economy: an Econometric Analysis. Economic Modelling 32, 400-428.
Diebold F.X. (1997). The Past, Present, and Future of Macroeconomic Forecasting. National Bureau of Economic Research w6290.
Gurvich E.T., Sokolov V., Ulyukaev A.V. (2008) The Impact of the Balassa-Samuelson Effect on the Real Ruble Exchange Rate: The Assessment. Voprosy Ekonomiki 7, 12-30 (in Russian).
Ivashchenko S.M. (2013). Dynamic Stochastic General Equilibrium Model with Banks and Endogenous Defaults of Firms. Journal of the New Economic Association 19, 3, 27-50 (in Russian).
Kehoe T.J. (2005). An Evaluation of the Performance of Applied General Equilibrium Models of the Impact of NAFTA. In: "Frontiers in Applied General Equilibrium Modeling" Kehoe T.J., Srinivasan T., Whalley J. (eds.). New York: Cambridge University Press, 341-377.
Makarov V.L. (1999). A Computable Model of Russian Economy (RUSEC). Preprint No. WP/99/069. Moscow: CEMI RAS (in Russian).
Makarov V., Aivasian S., Borissova S., Lakalin E. (2001). Econometric Model of the Russian Economy for Short-Term Forecasting and Scenario Analysis. Working paper WP/2001/121. Moscow: CEMI RAS (in Russian).
Makarov V.L., Bakhtizin A.R., Bakhtizina N.V. (2006). Agent-Based Model of Russian Socio-Economic System (CGE Model with Built-in Neural Networks Approach). Internet journal "Artificial societies" 1, 1. Available at: (accessed: March 2016).
Meltzer A.H. (1995). Monetary, Credit and (Other) Transmission Processes: a Monetarist Perspective. The Journal of Economic Perspectives 9, 49-72.
Merlevede B., Schoors K., Aarle B. van (2009). Russia from Bust to Boom and Back: Oil Price, Dutch Disease and Stabilisation Fund. Comparative Economic Studies 51(2), 213-241.
Polbin A.V. (2013). Development of a Dynamic Stochastic General Equilibrium Model for an Economy with High Dependence on Oil Export. The HSE Economic Journal 17(2) (in Russian).
Shulgin A.G. (2014). How Much Monetary Policy Rules Do We Need to Estimate DSGE Model for Russia? Applied Econometrics 4, 3-31 (in Russian).
Stock J.H. (1987). Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors. Econometrica 5, 1035-1056.

Struchenkov V.I. (Moscow) Mathematical models and algorithms for optimal planning of reproduction and use of renewable bioresources
Economics and mathematical methods
, 2016, 52 (3), 114-124.
We study the problem of optimal planning of the renewable bioresources implementation, namely the commercial breeding of fish and animals. We are studying different models of the objective function, which is the difference between income for the entire planning period and the cost of using the resource, including extraction. The unknowns are the annual volumes of resources used. There may be restrictions on the minimum size of these volumes, as well as restrictions on the minimum amount of a resource that should remain after the end of the reporting period of planning. For the simple linear model it shows that every year except the last, we should use the minimum allowable amount of resources, and in the last year to use the maximum amount of the resource, i.e. to leave for further work specified minimum volume. For the quadratic model based on dynamic programming method we derived new formulas, thus avoiding sorting options step by step solutions. For any additive objective function new efficient algorithms are offered for solving the problem using the Pareto sets.
Keywords: resource, the objective function, the set of states, dynamic programming, the optimal path, Pareto sets.
JEL Classification: C610.
REFERENCES (with English translation or transliteration)
Bellman R.E., Dreyfus S.E. (1962). Applied Dynamic Programming. Princeton: Princeton University Press.
Kosorukov O.A., Mishchenko A.V. (2003). Operation Study. Moscow: Ekzamen (in Russian).
Mentushkin V.V., Kislakov Yu.Ya. (1967). Fish Breeding Optimization Using the Method of Dynamic Programming. Fishery 7, 79-81 (in Russian).
Soldatov M.A. (2005). Economic - Mathematical Modeling of Optimal Fishing off Control of Fishery Resources. Proceedings Don NTU. Series: Economic 100-1, 184-190 (in Russian).
Struchenkov V.I. (2010). Dynamic Programming with Pareto Sets. Journal of Applied and Industrial Mathematics 4, 3, 428-430.


Vol. 52, No. 4

Glaz'ev S.Yu., Goridko N.P., Nizhegorodtsev R.M. (Moscow) The critics of Irving Fisher's formula and some illusions about contemporary monetary policy.
Economics and mathematical methods
, 2016, 52 (4), 3-23.
The paper gives a theoretical and calculable refusal of Irving Fisher's Formula used by monetarist economists for proving the way of overcoming inflation through monetary volume restriction. The paper proves that Formula is a linearized approximation for non-linear relations in real economic systems. It implements regression models of a middle-run non-linear interrelation between monetary volume and inflation rate (Goridko's Curve) based on statistical data for several countries during the recent 15 years. It deploys the concept of NSEGRI (non-slowing economic growth rate of inflation) on the basis of non-linear regression models relating GDP growth to the rate of inflation. The models linking GDP with monetary volume permit to discuss 'undermonetization' and 'overmonetization' of the economy for the cases of several countries. The implication is that one of essential sources of non-linearity for those middle-run relations is inevitability of innovative shifts. The paper provides comparative analysis of monetary policies in some countries whose aims and positions in the global economy are rather different. There are some conclusions for current monetary policies in Russia.
Keywords: monetary policy, Irving Fisher's Formula, Goridko's Curve, NSEGRI, monetization of economy, economic growth.
JEL Classification: E52, F43, O23, C51.
REFERENCES (with English translation or transliteration)
Barro R.J., Sala-i-Martin X. (1995). Economic Growth. Cambridge: MIT Pressð.
Bruno M., Easterly W. (1995). Inflation Crises and Long-Run Growth: NBER Working Papers 5209. National Bureau of Economic Research, Inc. Available at:›papers/w5209 (accessed: May 2016).
Dzyuba M.V., Nizhegorodtsev R.M. (2010). Modeling Inflation Using Regression Analysis (for Example the Republic of Kazakhstan). Part 2. Terra Economicus 8, 4, 35-39 (in Russian).
Glaz'ev S.Yu. (2010a). Problems of Realization of Intellectual Capacities under Transition Towards the Innovative Development. In: "Non-economic edges of economy: unknown interrelations. Scientific and journalistic notes of social scientists". Moscow: Institut E'konomicheskix Strategij (in Russian).
Glaz'ev S.Yu. (2010b). The Strategy of Outstripping Development of Russia under the Global Crisis. Moscow: E'konomika (in Russian).
Glaz'ev S.Yu. (2015b). On Inflation Targeting. Voprosy Economiki 9, 124-135 (in Russian).
Glaz'ev S.Yu. (2015c). Experiments at the Cost of Sovereignty. Expert 28, 34-38 (in Russian).
Glaz'ev S.Yu. (2015d). The Glitter and Poverty of the Russian Monetarists. Economic Science of Contemporary Russia 2, 7-21; 3, 7-25 (in Russian).
Glaz'ev S.Yu. (2015à). On Urgent Measures to Strengthen the Economic Security of Russia and the Withdrawal of the Russian Economy on a Trajectory of Advancing Development. Report. Moscow: Institut e'konomicheskix strategij, Russkij biograficheskij institut (in Russian).
Goridko N.P. (2011a). Multifactor Models of Inflation: the Case of Ukraine. In: "Banking system of Ukraine under globalization of financial markets". Abstracts and presentations. Transactions of International research conference, October, 20-21, 2011. Cherkassy: Izdatel' Yu.A. Chabanenko, 319-321 (in Russian).
Goridko N.P. (2011b). Multifactor Lagged Models of Inflation. In: "Control for Innovations - 2011". Transactions of International research conference, November, 14-16, 2011. R.M. Nizhegorodtsev (ed.). Moscow: LENAND, 368-373 (in Russian).
Goridko N.P. (2012). Regression Modelling of Inflation. Moscow: RosNOU (in Russian).
Goridko N.P. (2014). Factors of Money Supply and Monetary Policy in the Stagnative Economy. Drukerovskij vestnik 4, 114-124 (in Russian).
Goridko N.P. (2016). Modeling of Non-Slowing Economic Growth Rate of Inflation (NSEGRI) for Russian Economy. Drukerovskij vestnik 3, 78-88 (in Russian).
Goridko N.P., Nizhegorodtsev R.M. (2012à). Interrelation between Emissive and Transmissive Mechanisms of Inflation in Contemporary Ukrainian Economy: the Experience of Regressional Modelling. National Bank of Ukraine Bulletin 6, 22-26 (in Russian).
Goridko N.P., Nizhegorodtsev R.M. (2012á). Factor Regression Modelling of Real Cost of Financial Assets for Russia. Transactions of XIII International research conference 'IT: Advance and Applications'. Vladikavkaz: Flamingo, 75-88 (in Russian).
Kudrin A. (2007). Inflation: Russian and Global Trends. Problems of Economics 10, 4-26 (in Russian).
Lebedev O. (2013). The Global Financial and Economic Crisis of the Year 2008. Available at: (accessed: May 2016, in Russian).
Medvedev Called the Delay of the Indexation of Pensions as a "Temporary Measure" (2016). Available at: (accessed: May 2016, in Russian).
Nizhegorodtsev R., Goridko N. (2015). The Impact of Money Supply on Economic Growth: Theory, Experience, Modelling. Handbook on the Economics, Finance and Management Outlooks 3, 66-72. ISBN 978-969-9952-03-6). Available at: (accessed: May 2016).
Nizhegorodtsev R.M. (2006). Inflation Control Problems: Contemporary Approaches. Problemy Upravleniya 6, 25-30 (in Russian). Nizhegorodtsev R.M. (2007). Current Inflation: Forms, Factors, Implications and Remedies. Gomel': Centr issledovaniya institutov rynka (in Russian).
Nizhegorodtsev R.M., Goridko N.P. (2012à). Regression Modeling of Dynamics of Real Cost of Financial Assets (on an Example of Ukraine). Financial Analytics: Science and Experience 14, 33-40 (in Russian).
Nizhegorodtsev R.M., Goridko N.P. (2012á). Monetary Policies and Outlooks for Economic Growth: Lessons from the Crisis, Models, Forecasts. In: "Economic Security of Contemporary Russia: Lessons from Crisis and Outlooks for Growth". V.A. Chereshneva, A.I. Tatarkina, M.V. Fedorova (eds.). Vol. 1. Ekaterinburg: Institut e'konomiki UrO RAN, 831-877 (in Russian).
Nizhegorodtsev R.M., Goridko N.P., Shkodina I.V. (2014). Institutional Principles of Finance Theory: Modern Approaches. Moscow: INFRA-M (in Russian).
Osnovnye napravleniya edinoj gosudarstvennoj denezhno-kreditnoj politiki na 2016 god i period 2017 i 2018 godov (2015). Moscow: CB RF. Available at: (2017-2018).pdf (accessed: May 2016, in Russian).
Osoboe mnenie chlena Nacional'nogo bankovskogo soveta S.Yu. Glaz'eva po proektu re-sheniya NBS "Ob osnovnyx napravleniyax edinoj gosudarstvennoj denezhno-kreditnoj politi-ki na 2013-2015 gg." (2012).
Osoboe mnenie chlena Nacional'nogo finansovogo soveta S.Yu. Glaz'eva po proektu re-sheniya NFS "Ob osnovnyx napravleniyax edinoj gosudarstvennoj denezhno-kreditnoj politi-ki na 2014-2016 gg." (2013).
Osoboe mnenie chlena Nacional'nogo finansovogo soveta S.Yu. Glaz'eva po proektu re-sheniya NFS "Ob osnovnyx napravleniyax edinoj gosudarstvennoj denezhno-kreditnoj politi-ki na 2015-2017 gg." (2014).
Paydiev L. (2009). What Will the Economy of a New World Be? Available at: (publishing on 29.04.2009).
Polyakova O.V., Goridko N.P. (2012). Factor Regressional Analysis of Inflation in Russian Economy for 1999-2010 Years. RISK: Resursy. Informaciya. Snabzhenie. Konkurenciya. Moscow: OAO "ITKOR" 3, 193-199 (in Russian).
Schumpeter J. (1939). Business Cycles. A Theoretical, Historical and Statistical Analysis of Capitalist Process. N.Y.: McGraw-Hill. The State and the Market: New Quality of Interaction in Information-Network Economy (2007). S.A. Dyatlov, D.Yu. Miropol'skiy, V.A. Plotnikov (eds.). Saint Petersburg: Asterion (in Russian).

Aivazian S.A., Bereznyatskiy A.N., Brodsky B.E. (Moscow) Econometric models of regional consumer price indices.
Economics and mathematical methods
, 2016, 52 (4), 24-46.
Multivariate econometric models of Russian inflation are proposed in this paper. Consumer price index is used to quantify inflationary processes. Monetary and non-monetary variables are examined in the models. The authors consider foreign exchange rate of the ruble as monetary factor and government regulation of prices for certain goods and services and food market condition as non-monetary. Special attention is paid to a regional aspect of the problem. The question is whether estimates of parameters of the models are stable and statistically significant at the level of regional consumer price indices. The key result is statistical significance of models for the majority of the regions.
Keywords: consumer price index, inflation, Russian regions, econometric models of price indices.
JEL Classification: E31, E37, R15.
REFERENCES (with English translation or transliteration)
Bereznytsky A.N., Brodsky B.E. (2012). Structural Breaks Analysis in the Russian Inflation Model. In: "Multivariate statistical analysis and econometrics". Proceedings of VIIIth International School-Seminar. By ed. S.A. Aivazian. Town of Tsakhadzor, The Republic of Armenia. M.: CEMI RAS (in Russian).
Brown M., Haas R. de, Sokolov V. (2013). Regional Inflation and Financial Dollarisation. European Bank for Reconstruction and Development. Working papers 163.
Danilova I.V., Rezepin A.V. (2009). Implementation of Inflation Targeting Policy in Russia: Regional Conditions Differentiations. Bulletin of the South Ural State University. Series "Economics and Management" 7(183), 11-19 (in Russian).
Gluschenko K. (2001). Inter-Regional Variability of Inflation Rates. Economics Education and Research Consortium. Working Paper Series 99/17.
Gluschenko K. (2010). Price Convergence and Market integration in Russia. William Davidson Institute. Working Paper Number 999.
Gluschenko K. (2013). Distribution Dynamics of Russian Regional Prices. William Davidson Institute. Working Paper Number 1061.
Kadyrov Ì.Ò. (2010). Impact of Exchange Rate on Prices in the Presence of Structural breaks. Applied Econometrics 3(19), 9-22 (in Russian).
Kataranova Ì. (2010). Relationship between Exchange Rate and Inflation in Russia. Voprosy Economiki 1, 44-62 (in Russian).
Kiseleva P.S., Ilyashenko V.V. (2012). Interregional Differentiation of the Rate of Inflation in Russia. Journal of the Ural State University of Economics (Izvestiya Uralskogo gosudarstvennogo ekonomicheskogo universiteta) 1(39), 5-10 (in Russian).
Kiseleva P.S., Ilyashenko V.V. (2015). Factors and Dynamics of Inflationary Processes in Industrial Region. Journal of the Ural State University of Economics (Izvestiya Uralskogo gosudarstvennogo ekonomicheskogo universiteta) 3(59), 24-29 (in Russian).
Nikolic M. (2006). Monetary Policy in Transition. Inflation Nexus Money Supply in Postcommunist Russia. London: Palgrave Macmillan. Oomes N., Ohnsorge F. (2005). Money Demand and Inflation in Dollarized Economies: the Case of Russia. IMF Working Paper. WP/05/144.
Guidelines for the Single State Monetary Policy in 2003 (2002). Moscow: Bank of Russia (in Russian).
Guidelines for the Single State Monetary Policy in 2006 (2005). Moscow: Bank of Russia (in Russian).
Ponomarenko A. (2016). A Note on Money Creation in Emerging Market Economies. Bank of Russia Working Paper Series 10, 5-18.
Ponomarev Y., Trunin P., Ulyukayev A. (2014). Exchange Rate Pass-through in Russia. Voprosy Economiki 3, 21-35 (in Russian).
Shmykova S.V., Sosunov K.A. (2005). The Responsiveness of Consumer Prices to Exchange Rate in Russia. The HSE Economic Journal 1, 3-16 (in Russian).
Shumetov V.G. (2014). Analysis of Interregional Differences in Inflationary Developments in the Economy of Central Russia. Studies on Russian Economic Development 1(25), 91-98.
Sosunov K., Zamulin O. (2007). Monetary Policy in an Economy Sick with Dutch Disease. CEFIR/NES. Working Paper series 101.
Trunin P.V., Vashchelyuk N.V. (2015). The Analysis of Money Supply Endogeneity in Russia. Journal of the New Economic Association 1(25), 103-131 (in Russian).
Vdovichenko A., Voronina V., Dynnikova O., Subbotin V., Ustinov A. (2003). Inflation and Exchange Rate Policy. Voprosy Economiki 12, 39-55 (in Russian).
Vdovichenko A.G. (2003). Inflation or the Ruble's Appreciation: Which Worse Less? Banking 10, 4-6 (in Russian).

Istratov V.A. (Moscow) Modelling norm emergence in social sciences.
Economics and mathematical methods
, 2016, 52 (4), 47-73.
The article compares both theories of social norm emergence and social norm interpretations that are wide spread in economics including game theory, sociology, psychology, law and agent-based simulation. Particular attention has been given to the modelization potential of the addressed theories which largely depends on the presentation of the theories and to what degree they are formalized. Despite the variety of approaches and interpretations in different sciences a strong mutual influence among them is obvious. This helps us to bring out a common mechanism of social norm formation which is described in the concluding part of the paper. The results will be of help in understanding and simulating, primarily within agent-based paradigm, of socio-economic interrelations.
Keywords: institution, social norm, game theory equilibrium, personal norm, convention, behavior, sanction, agent-based modelling.
JEL Classification: E02, E03, C70.
REFERENCES (with English translation or transliteration)
Axelrod R. (1986). An Evolutionary Approach to Norms. The American Political Science Review 80, 4, 1095-1111.
Boella G., Torre L. van der, Verhagen H. (2008). Introduction to the Special Issue on Normative Multiagent Systems. Autonomous Agents and Multi-Agent Systems 17, 1, 1-10.
Cialdini R.B., Trost M.R. (1998). Social Influence: Social Norms, Conformity, and Compliance. In: "The handbook of social psychology" Gilbert D.T., Fiske S.T., Lindzey G. (eds.). Vol. 2. Boston: McGraw-Hill, 151-192.
Coleman J.S. (1990). Foundations of Social Theory. Cambridge: Belknap Press.
Conte R., Castelfranchi C. (1995). Understanding the Functions of Norms in Social Groups Through Simulation. In: Gilbert N., Conte R. (eds.) "Artificial Societies: the Computer Simulation of Social Life". L.: UCL Press, 252-267.
Conte R., Castelfranchi C. (1993). Norms as Mental Objects: from Normative Beliefs to Normative Goals. In: "Reasoning about Mental States: Formal Theories & Applications. Technical Report SS-93-05" Horty J., Shoham Y. (eds.). Menlo Park: The AAAI Press, 40-47.
Cooter R.D. (1996). Decentralized Law for a Complex Economy: the Structural Approach to Adjudicating the New Law Merchant. University of Pennsylvania Law Review 144, 5, 1643-1696.
Ellickson R.C. (2001). The Market for Social Norms. American Law and Economics Review 3, 1, 1-49.
Elsenbroich C., Gilbert N. (2014). Modelling Norms. Dordrecht: Springer Science, Business Media.
Elster J. (1989). Social Norms and Economic Theory. Journal of Economic Perspectives 3, 4, 99-117.
Epstein J.M. (2001). Learning to be Thoughtless: Social Norms and Individual Computation. Computational Economics 18, 1, 9-24.
Fishbein M., Ajzen I. (1975). Belief, Attitude, intention, and Behavior: an Introduction to Theory and Research. Reading: Addison-Wesley.
Granberg A.G. (1988). Modelling of Socialist Economy. Moscow: E'konomika (in Russian).
Horne C. (2001). Sociological Perspective on the Emergence of Social Norms. In: M. Hechter, K.-D. Opp (eds.) "Social norms". N.Y.: Russell Sage Foundation, 3-35.
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Drobysh I.I. (Moscow) Comparative analysis of market risk estimation methods based on 'value at risk'.
Economics and mathematical methods
, 2016, 52 (4), 74-93.
The article analyzes application of different Value at Risk methods (VaR) for market risk estimation in conditions of the Russian economy. The author has analyzed time series, which demonstrates the dynamics of daily logarithmic returns of the mutual fund, allocating funds in stocks of Russian leading companies for the years 2000-2014 - tested the hypothesis of normal distribution of logarithmic returns of the mutual funds. In some periods (for example, 2000 and 2002 years) the series of logarithmic returns well approximated by a normal distribution function, but in case of testing data on the whole of period the hypothesis of the normal distribution should be rejected. For estimation VaR are considered: delta-normal method (and its variations), historical simulation method, and hybrid Hull and White method. Examination of VaR methods accuracy and methods comparison is made by verifying methods based on historical data, tests includes the method of the Basel Committee, the Kupiec test, Christoffersen test, the loss function method. It examines: number of excesses, which VaR method shows (events, when the absolute value of the loss exceeds the VaR), the independence of the excess events from each other, as well as the average exceedance of the actual loss over VaR. Delta-normal method shows unstable results in the non-stationary conditions of the Russian economy. Historical simulation method and the Hull and White method show good stable results during the whole time interval under testing by the Basel Committee method and the Kupiec test (number of excesses). All VaR methods have property of clustering of the excess events (Christoffersen test shows negative results). The Hull and White method shows the lowest average exceedance of the actual loss over VaR, this method by comparison with other methods is most accurate.
Keywords: risk, asset value, economic losses, capital charge for market risk, value at risk, quantile of distribution function, programs.
JEL Classification: C000, C130, D810.
REFERENCES (with English translation or transliteration)
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Morozov S.L. (Moscow) Six universal accounting quarter plans.
Economics and mathematical methods
, 2016, 52 (4), 94-114.
It is offered to translate existing Gregorian and Julian 12-month's calendars simultaneously from the passive form in active (having fixed the beginning of year intercalary day transfer in the end of the year for December from February), and to make its absolutely exact, having entered a calendar constant a = 96,875/400 = 31/128 = 0,2421875 = µ = const = ÊÏ days instead of traditional accuracy a = 97/400 = 31,04/128 = 0,2425 days in a Gregorian calendar, and instead of accuracy a = 100/400 = 32/128 = 0,25 days, in Julian calendar that becomes only purely mathematical and does not result in any material inputs. Then both existing nowadays a calendar will cease to disperse among them and thus calendar church split 1582 between Catholic and Orthodox faiths will be liquidated. In the simplest case, it is possible to be limited to the existing passive form of a calendar, but with obligatory transition on absolutely exact a calendar constant. The author suggests these new ultraprecise absolutely coordinated mathematical Christian calendars to name Franciscan Catholic and Kirillian Orthodox. The author has resulted all the main (cores) 13 calendar systems of modern mankind to uniform (purely mathematical global or universal) a digital reference Exchange Active (Astronavigating) Calendar (Quantum) Matrix (EACM) which can become eternal uniform Abrahamic or a Universal calendar of mankind [uniform (global or universal) digital reference Exchange Activ (Astronavigating) Calendar (Quantum) Matrix (EACM)].
Keywords: uniform time of Space civilization, Kirillian calendar, Franciscan calendar, partial 12-months and full 13-months, quarter constant, main quantum condition.
JEL Classification: C60, F55, F59.
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