

Mathematical Economics, Mathematical Finance, Random dynamical systems, Stochastic optimization and games.
Membership in learned societies
Society for the Advancement of Economic Theory, Founding Fellow, since 2011.
Moscow Mathematical Society, elected in 1989.Main directions of current research
Evolutionary Behavioural Finance
Von NeumannGale dynamical systems with applications in economics and finance
Gametheoretic analysis in economics
Some themes of past research
Equilibrium, growth and local interactions: An approach based on the Polterovich model
Topics in Mathematical Finance: Asset pricing, arbitrage, and volatilityinduced growth
Measurable selections and regular expectations
Markov fields and variational problems
Stochastic programming with applications in economics, finance and insurance
Organisational activities
Trimester Program "Stochastic Dynamics in Economics and Finance", Hausdorff Research Institute for Mathematics, Bonn, May  August 2013. Coorganised with R. Amir and K.R. SchenkHoppé. Poster
1st Manchester conference Mathematical Economics and Finance, 68 July 2017.
2nd Manchester conference Mathematical Economics and Finance, 1718 December 2017.
3rd Manchester conference Mathematical Economics and Finance, 12 September 2019.
Monographs
Stochastic models of control and economic dynamics. Academic Press, London, 1987 (with V.I. Arkin).
Markov fields over countable partially ordered sets: Extrema and splitting. Memoirs of Amer. Math. Soc., v. 112 (537), 1994 (with P.E. Greenwood).
Textbook
Mathematical Financial Economics: A Basic Introduction (with T. Hens and K.R. SchenkHoppé), Springer, June 2015. Front matter. Springer website
Working papers
Unbeatable strategies, Economics Discussion Paper Series EDP2101, January 2021 (with R. Amir and V. Potapova).
Forthcoming
Evolution in Pecunia, to appear in Proc. Nat. Acad. Sci. USA, Special Issue "Evolutionary Models of Financial Markets", S. Levin, ed., 2021 (with R. Amir, T. Hens, V. Potapova and K.R. SchenkHoppé).
Published papers
A multidimensional Fatou lemma for conditional expectations, 2021, Positivity, published online 29 March 2021 (with E. Babaei and K.R. SchenkHoppé). Viewonly pdf file
Behavioral equilibrium and evolutionary dynamics in asset markets, 2020, Journal of Mathematical Economics, 91, 121135 (with T. Hens, V. Potapova and K.R. SchenkHoppé). Open access publication: PDF
An evolutionary finance model with a riskfree asset, 2020, Annals of Finance, 16, 593607 (with S. Belkov and T. Hens). DOI
An evolutionary finance model with short selling and endogenous asset supply, 2020, Economic Theory, published online 8 May 2020 (with R. Amir, S. Belkov and T. Hens). DOI
Von NeumannGale model, market frictions, and capital growth, 2020, Stochastics, published online 31 Jan 2020 (with E. Babaei, K.R. SchenkHoppé and M.V. Zhitlukhin). DOI
Von NeumannGale dynamics and capital growth in financial markets with frictions, 2020, Mathematics and Financial Economics, 14, 283305 (with E. Babaei, K.R. SchenkHoppé and M.V. Zhitlukhin). Open access publication: PDF
Oligopoly with network effects: firmspecific versus single network, 2020, Economic Theory, published online 4 Oct 2019 (with R. Amir and Adriana Gama. ). DOI
Nash equilibrium strategies and survival portfolio rules in evolutionary models of asset markets, 2020, Mathematics and Financial Economics, 14, 249262 (with S. Belkov, T. Hens and L. Xu). DOI
Logoptimal and rapid paths in von NeumannGale dynamical systems, 2020, Journal of Mathematical Analysis and Applications, 481(2), published online 9 Sep 2019 (with E. Babaei and K.R. SchenkHoppé). DOI
Stochastic fixed points and nonlinear PerronFrobenius theorem, 2018, Proceedings of the American Mathematical Society, 146, 43154330 (with E. Babaei and S.A. Pirogov). DOI
A new look at the classical Bertrand duopoly, 2018, Games and Economic Behavior, 109, 99103 (with R. Amir). DOI
Correlated equilibrium in a nutshell, 2017, Theory and Decision, 83, 457468 (with R. Amir and S. Belkov). Viewonly pdf file
A new perspective on the classical Cournot duopoly, 2017, Journal of Dynamics and Games, 4, 361367 (with R. Amir). DOI
On Zermelo's theorem, 2017, Journal of Dynamics and Games, 4, 191194 (with R. Amir). DOI
Evolutionary behavioural finance. Handbook of Post Crisis Financial Modelling (E. Haven et al., eds.), Palgrave MacMillan, 2015, 214234 (with T. Hens and K.R. SchenkHoppé) DOI
Growthoptimal investments and numeraire portfolios under transaction costs, 2013, in: Handbook of the Fundamentals of Financial Decision Making ( L.C. MacLean and W.T. Ziemba, eds.), World Scientific, Singapore, pp. 789808 (with W. Bahsoun and M.I. Taksar).
Controlled random fields, von NeumannGale dynamics and multimarket hedging with risk, 2013, Stochastics, v. 85, 652666 (with M.V. Zhitlukhin).
Asset market games of survival: A synthesis of evolutionary and dynamic games, 2013, Annals of Finance, 9, 121144 (with R. Amir and K.R. SchenkHoppé).
Evolutionary finance and dynamic games, 2011, Mathematics and Financial Economics, v. 5, 161184 (with R. Amir, T. Hens and L. Xu ).
Local stability analysis of a stochastic evolutionary financial market model with a riskfree asset, 2011, Mathematics and Financial Economics, v. 5, 185202 (with T. Hens and K.R. SchenkHoppé).
Linearization and local stability of random dynamical systems, 2011, Proceedings of the American Mathematical Society, v. 139, 10611072 (with K.R. SchenkHoppé and S.A. Pirogov).
Almost sure Nash equilibrium strategies in evolutionary models of asset markets, Mathematical Methods of Operations Research, 2011, v. 73, 235250 (with W. Bahsoun and L. Xu ).
Survival and evolutionary stability of the Kelly rule, 2011, in: The Kelly Capital Growth Investment Criterion: Theory and Practice (L.C. MacLean, E.O. Thorp and W.T. Ziemba, eds.), World Scientific, Singapore, pp. 273284 (with T. Hens and K.R. SchenkHoppé).
Growing wealth with fixedmix strategies, 2011, in: The Kelly Capital Growth Investment Criterion: Theory and Practice (L.C. MacLean, E.O. Thorp and W.T. Ziemba, eds.), World Scientific, Singapore, pp. 427455 (with M.A.H. Dempster and K.R. SchenkHoppé).
Stochastic nonlinear PerronFrobenius theorem, 2010, Positivity, v. 14, 4357 (with S.A. Pirogov).
Arbitrage in stationary markets, 2009, Decisions in Economics and Finance, v. 32, 512 (with D. Kapoor).
Dynamic interaction models of economic equilibrium, 2009, Journal of Economic Dynamics and Control, v. 33, 166182 (with M.I. Taksar).
Evolutionary finance, 2009, in: Handbook of Financial Markets: Dynamics and Evolution (T. Hens and K.R. SchenkHoppé, eds.), a volume in the Handbooks in Finance series, W.T. Ziemba, ed., Elsevier, Amsterdam, pp. 507566 (with T. Hens and K.R. SchenkHoppé).
Globally evolutionarily stable portfolio rules, 2008, Journal of Economic Theory, v. 140, 197228 (with T. Hens and K.R. SchenkHoppé).
Rapid paths in von NeumannGale dynamical systems, 2008, Stochastics, v. 80, 129142 (with W. Bahsoun and M.I. Taksar.)
Financial markets. The joy of volatility, 2008, Quantitative Finance, v. 8, 13 (with M.A.H. Dempster and K.R. SchenkHoppé).
Stochastic equilibria in von NeumannGale dynamical systems, 2008, Transactions of the American Mathematical Society, v. 360, 33453364 (with K.R. SchenkHoppé).
A stochastic contraction principle, 2007, Random Operators and Stochastic Equations, v. 15, 155162 (with S.A. Pirogov).
Volatilityinduced financial growth, 2007, Quantitative Finance, v. 7, 151160 (with M.A.H. Dempster and K.R. SchenkHoppé). Reprinted in: Quantitative Fund Management, M.A.H. Dempster, G. Mitra and G. Pflug, eds., Chapman and Hall / CRC Financial Mathematics Series (Taylor and Francis Group), 2009, 6784.
Pure and randomized equilibria in the stochastic von NeumannGale model, 2007, Journal of Mathematical Economics, v. 43, 871887 (with K.R. SchenkHoppé).
Asset pricing and hedging in financial markets with transaction costs: An approach based on the von NeumannGale model, 2006, Annals of Finance, v. 2, 327355 (with M.A.H. Dempster and M.I. Taksar).
The von NeumannGale growth model and its stochastic generalization, 2006, in: Handbook on Optimal Growth, R.A. Dana, C. Le Van, T. Mitra and K. Nishimura, eds., Springer, New York, 337383 (with K.R. SchenkHoppé).
Evolutionary Stable Stock Markets, 2006, Economic Theory, v. 27, 449468 (with T. Hens and K.R. SchenkHoppé).
Market selection and survival of investment strategies, 2005, Journal of Mathematical Economics, Special Issue on Evolutionary Finance, v.41, 105122 (with R. Amir, T. Hens and K.R. SchenkHoppé).
On the Fundamental Theorem of Asset Pricing: Random constraints and bangbang noarbitrage criteria, 2004, Mathematical Finance, v.14, 201221 (with K. Schuerger and M.I. Taksar).
Noncooperative versus cooperative R&D with endogenous spillover rates, 2003, Games and Economic Behavior, v. 42, 183207 (with R. Amir and J. Wooders).
Exponential growth of fixedmix strategies in stationary asset markets, 2003, Finance and Stochastics, v. 7, 263276 (with M.A.H. Dempster and K.R. SchenkHoppé).
From rags to riches: On constant proportions investment strategies, 2002, International Journal of Theoretical and Applied Finance, v. 5, 563573 (with K.R. SchenkHoppé).
Equilibrium states of random economies with locally interacting agents and solutions to stochastic variational inequalities, 2002, Annals of Operations Research, Special Issue ''Stochastic Equilibrium Problems in Economics and Game Theory'', v. 114, 145165 (with M.I. Taksar).
Market selection of financial trading strategies: Global stability, 2002, Mathematical Finance, v. 12, 329339 (with T. Hens and K.R. SchenkHoppé).
Convex stochastic duality and the ''biting lemma'', 2002, Journal of Convex Analysis, v. 9, 237244 (with S.D. Flåm).
Sharing nonconvex costs, 2001, Journal of Global Optimization, Special Issue on Applications to Economics, v. 20, 257271 (with S.D. Flåm).
Convex stochastic optimization for random fields on graphs: A method of constructing Lagrange multipliers, 2001, Mathematical Methods of Operations Research, v. 54, 217237 (with M.I. Taksar).
Rapid growth paths in convexvalued random dynamical systems, 2001, Stochastics and Dynamics, v. 1, 493509 (with M.I. Taksar).
Stochastic programming: Nonanticipativity and Lagrange multipliers, in: Encyclopedia of Optimization, Kluwer Academic Publishers, Dordrecht, 2001, v. 4, 332338 (with S.D. Flåm).
On Dynkin's model of economic equilibrium under uncertainty, 2001, Economics Bulletin, v. 3, 18 (with G. Carlier).
A functional central limit theorem for equilibrium paths of economic dynamics, 2000, Journal of Mathematical Economics, v. 33, 8199 (with R. Amir).
Turnpike theorems for positive multivalued stochastic operators, 2000, Advances in Mathematical Economics, v. 2, 120 (with S. Anoulova and V.M. Gundlach).
Robust insurance mechanisms and the shadow prices of information constraints, 1999, Journal of Applied Mathematics and Decision Sciences, v. 3, 85128 (with W.K. Klein Haneveld and L.J. Mirman).
Convexvalued random dynamical systems: A variational principle for equilibrium states, 1999, Random Operators and Stochastic Equations, v. 7, 2338 (with L. Arnold and V.M. Gundlach).
Stochastic version of Polterovich's model: Exponential turnpike theorems for equilibrium paths, 1999, Macroeconomic Dynamics, v. 3, n. 2, 149166 (with R. Amir).
Rapid growth paths in multivalued dynamical systems generated by homogeneous convex stochastic operators, 1998, SetValued Analysis, v. 6, 6182 (with S.D. Flåm).
Balanced states in stochastic economies with locally interacting agents, 1998, Stochastics, v. 64, 235253 (with M.A.H. Dempster and S.A. Pirogov).
The turnpike property and the central limit theorem in stochastic models of economic dynamics, 1997, in: Statistics and Control of Stochastic Processes, The Liptser Festschrift, Yu.M. Kabanov, B.L. Rozovskii, and A.N. Shiryaev, eds., World Scientific, Singapore  New Jersey  London, 63101 (with S.D. Flåm).
Noncooperative games in networks: Stability and sensitivity of equilibria, 1997, in: Complementarity and Variational Problems: State of the Art, M.C. Ferris and J.S. Pang, eds., SIAM, Philadelphia, 6275 (with S.D. Flåm).
Metonymy and cross section demand, 1997, Journal of Math. Economics, v. 28, 397414 (with W. Hildenbrand and M. Jerison).
Selected publications prior to 1997
Turnpike theorems for stochastic equilibria on graphs, 1996, in: Operations Research Proceedings 1995, P. Kleinschmidt et al., eds., SpringerVerlag, Berlin  Heidelberg  N.Y., 241245 (with M.A.H. Dempster and S.A. Pirogov).
The shortest path around an island outside the shallows, 1995, Markov Processes and Related Fields, v. 1, 407418.
Stochastic equilibria on graphs, 1995, II, Journal of Math. Economics, v. 24, 383406 (with M.I. Taksar).
Stochastic equilibria on graphs, 1994, I, Journal of Math. Economics, v. 23, 401433 (with M.I. Taksar).
A limit theorem for random matrices with a multiparameter, 1994, Stochastic Processes and their Appl., v. 52, 6574 (with K. Schuerger).
Regular conditional expectations and the continuum hypothesis, in: The Dynkin Festschrift, Birkhauser, Boston, 1994, 8593.
Stochastic extrema, splitting random elements and models of crack formation, in: System Modelling and Optimization, Proc. of the 16th IFIPTC7 Conf. (Compiègne, July 59, 1993), Lecture Notes in Control and Inform. Sci., No. 197, SpringerVerlag, London, 1994, 315319 (with P.E. Greenwood).
Controlled random fields on graphs and stochastic models of economic equilibrium, 1991, in: New Trends in Probability and Statistics (Volume in Honour of Yu. V. Prohorov), VSP, Utrecht, 391412.
The method of monotone operators in the stochastic theory of economic equilibrium, 1990, Matekon, v. 26, n. 3, Sharpe Publ., N.Y., 2143.
Stochastic extremal problems and the strong Markov property of random fields, 1988, Uspekhi Matem. Nauk (Russian Math. Surveys), v. 43, n. 2, 341.
Measurable images of compact spaces and selectors of analytic sets, 1988, Doklady AN SSSR (Soviet Math. Dokl.), v. 299, n. 3, 538541.
Controlled random fields on a directed graph, 1988, Teor. Ver. i Primen. (Theory of Probab. and Appl.), v. 33, n. 3, 465479.
Random sets and Markov fields (Invited paper), 1987, in: Proc. of the 1st World Congress of the Bernoulli Soc.,Tashkent, Sept. 1986. Utrecht, VNU, 339344.
Measurable selection theorems and stochastic control models in general topological spaces, 1986, Mat. Sbornik (Math. USSR Sbornik), v. 131, n. 1, 2739.
Regular conditional expectations of random variables depending on parameters, 1986, Teor. Ver. i Primen. (Theory of Probab. and Appl.), v. 31, n. 3, 586589.
Equilibrium states of monotone operators and equilibrium trajectories in stochastic economic models, 1986, Lect. Notes Control Inf. Sci., n. 81, 334338.
Stochastic models of economic dynamics and equilibrium: Asymptotic behaviour of equilibrium paths, 1984, in: Proc. of the Seventh Conf. on Probab. Theory (Brasov 1982), Bucharest, 149158 (with P.K. Katyshev).
An optimality principle and an equilibrium theorem for controlled random fields on a directed graph, 1984, Doklady AN SSSR (Soviet Math. Dokl.), v. 274, n. 4, 782786.
Strong Markov property and splitting elements for random fields over a partially ordered set, 1983, Teor. Ver. i Primen. (Theory of Probab. and Appl.), v. 28, n. 4, 801802.
Probabilistic variant of the turnpike theorem for homogeneous convex controllable models, 1983, Math. Zametki (Math. Notes), v. 33, n. 1, 185194 (with S.E. Kuznetsov).
Models of economic growth taking account of random factors, 1982, Econ. i Mat. Metody, v. 18, n. 6, 11251132 (with S.E. Kuznetsov). (In Russian.)
A nonstationary stochastic analog of the von NeumannGale model of a developing economy: a theorem on a characteristic, 1981, Optimizatsya, v. 27, 3443. (In Russian.)
Equilibrium paths in probabilistic models of economic dynamics, 1982, Teor. Ver. i Primen. (Theory of Probab. and Appl.), v. 27, n. 1, 120 128 (with P.K. Katyshev).
Homogeneous convex models in the theory of controlled random processes, 1980, Doklady AN SSSR (Soviet Math. Dokl.), v. 253, n. 3, 524527.
Probabilistic modification of the von NeumannGale model, 1980, Uspekhi Matem. Nauk (Russian Math.Surveys), v. 35, n. 4, 185186 (with Yu.M. Kabanov).
Bounds for prices in models of economic development, 1980, Econ. i Mat. Metody, v. 16, n. 3, 592593. (In Russian.)
Measurable choice and the continuum axiom, 1978, Doklady AN SSSR (Soviet Math. Dokl.), v. 238, n. 1, 1114.
''Splitting times'' for random fields, 1978, Teor.Ver. i Primen. (Theory of Probab. And Appl.), v. 23, n. 2, 433438 (with A.I. Ovseevich).
Liftings and conditional distributions, 1977, in: Selected Topics in Probab.Theory and Math. Economics, Moscow, CEMI, 92113. (In Russian.)
''Markov times'' for random fields, 1977, Teor.Ver. i Primen. (Theory of Probab. and Appl.), v. 22, n. 3, 575581.
Turnpike theorems in stochastic models of economic dynamics, 1976, Mat. Zametki (Math. Notes), v. 19, n. 2, 279290.
Optimal economic planning under production uncertainty, 1976, Publ. économétr., v. 9, n. 1, 8198.
Lagrange multipliers for the problems of stochastic programming, 1976, Lect. Notes Econ. Math. Syst., n. 133, 3448.
Measurable selection and dynamic programming, 1976, Math. Oper. Res., v. 1, n. 3, 5255.
Regular conditional expectations of correspondences, 1976, Teor. Ver. i Primen.(Theory of Probab. and Appl.), v. 21, n. 2, 333347 (with E.B. Dynkin).
The space 2^{X} and Markov fields, 1976, Doklady AN SSSR (Soviet Math. Dokl.), v. 230, n. 1, 2225.
Models of economic dynamics taking account of indeterminacy in the operation of an industrial process, 1975, Doklady AN SSSR (Soviet Math. Dokl.), v. 223, n. 3, 537540.
Positive matrixvalued cocycles over dynamical systems, 1974, Uspekhi Matem. Nauk (Russian Math. Surveys), v. 29, n. 5, 219220.
Optimal stochastic programs and their supporting prices, 1974, in: Mathematical Models in Economics, Amsterdam, North Holland, 219252.
Optimal economic planning taking account of stationary random factors, 1972, Doklady AN SSSR (Soviet Math. Dokl.), v. 206, n. 5, 10401042.
Markov chains on a matrix group, 1971, Mat. Zametki (Math. Notes), v. 10, n. 2, 181186.