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Senior researcher
Southern Federal University
Professor
Institute of Mathematics, Mechanics, and Computer Science named after of I.I. Vorovich
Research interests:
decision making under uncertainty, optimal control, mathematical finance, online learning
Research projects:
Project of the Russian Science Foundation No.17-19-0138 "Development of a comprehensive theory of management of sustainable development of active systems" (leader: G. Ugolnitskiy) 2017-2019, 2020-2021.
Publications
Rokhlin, D.B., Ougolnitsky, G.A. Optimal Incentive Strategy in a Continuous Time Inverse Stackelberg Game (2020) Static and Dynamic Game Theory: Foundations and Applications, pp. 201-213. DOI: 10.1007/978-3-030-51941-4_13
Rokhlin, D.B. Robbins;Monro conditions for persistent exploration learning strategies (2019) Springer Proceedings in Mathematics and Statistics, 291, pp. 237-247. DOI: 10.1007/978-3-030-26748-3_14
Rokhlin, D.B. Q-learning in a stochastic stackelberg game between an uninformed leader and a naive follower (2019) Theory of Probability and its Applications, 64 (1), pp. 41-58. DOI: 10.1137/S0040585X97T989386
Rokhlin, D.B., Ougolnitsky, G.A. Optimal Incentive Strategy in a Markov Game with Multiple Followers (2019) Static and Dynamic Game Theory: Foundations and Applications, pp. 231-243. DOI: 10.1007/978-3-030-23699-1_12
Rokhlin, D.B., Usov, A. Asymptotic efficiency of the proportional compensation scheme for a large number of producers (2018) Yugoslav Journal of Operations Research, 28 (4), pp. 501-520. DOI: 10.2298/YJOR170918028R
Rokhlin, D.B., Ougolnitsky, G.A. Stackelberg Equilibrium in a Dynamic Stimulation Model with Complete Information (2018) Automation and Remote Control, 79 (4), pp. 701-712. DOI: 10.1134/S0005117918040112
Rokhlin, D.B. Minimax perfect stopping rules for selling an asset near its ultimate maximum (2017) Optimization Letters, 11 (8), pp. 1743-1756. DOI: 10.1007/s11590-016-1091-8
Ougolnitsky, G.A., Rokhlin, D.B., Usov, A.B. A two-level model of optimal harvesting under parameter uncertainty (2017) Far East Journal of Mathematical Sciences, 102 (7), pp. 1365-1380. DOI: 10.17654/MS102071365
Rokhlin, D.B. Asymptotic sequential Rademacher complexity of a finite function class (2017) Archiv der Mathematik, 108 (3), pp. 325-335. DOI: 10.1007/s00013-016-1002-3
Rokhlin, D.B., Usov, A. Rational taxation in an open access fishery model (2017) Archives of Control Sciences, 27 (1), pp. 5-27. DOI: 10.1515/acsc-2017-0001
Rokhlin, D.B., Mironenko, G. Optimal production and pricing strategies in a dynamic model of monopolistic firm (2016) Japan Journal of Industrial and Applied Mathematics, 33 (3), pp. 557-582. DOI: 10.1007/s13160-016-0235-7
Rokhlin, D.B., Mironenko, G. Regular finite fuel stochastic control problems with exit time (2016) Mathematical Methods of Operations Research, 84 (1), pp. 105-127. DOI: 10.1007/s00186-016-0536-2
Rokhlin, D.B. Central limit theorem under uncertain linear transformations (2015) Statistics and Probability Letters, 107, pp. 191-198. DOI: 10.1016/j.spl.2015.08.027
Rokhlin, D.B. Central limit theorem under variance uncertainty (2015) Electronic Communications in Probability, 20, статья N 66, 10 p. DOI: 10.1214/ECP.v20-4341
Rokhlin, D.B. Verification by Stochastic Perron's Method in stochastic exit time control problems (2014) Journal of Mathematical Analysis and Applications, 419 (1), pp. 433-446. DOI: 10.1016/j.jmaa.2014.04.062
Rokhlin, D.B. Stochastic Perrons method for optimal control problems with state constraints (2014) Electronic Communications in Probability, 19, 15 p. DOI: 10.1214/ECP.v19-3616
Rokhlin, D.B. On the game interpretation of a shadow price process in utility maximization problems under transaction costs (2013) Finance and Stochastics, 17 (4), pp. 819-838. DOI: 10.1007/s00780-013-0206-7
Rokhlin, D.B. On the dynamic programming principle for controlled diffusion processes in a cylindrical region (2013) Siberian Electronic Mathematical Reports, 10, pp. 302-310.
Rokhlin, D.B. Recurrence relations for price bounds of contingent claims in discrete time market models (2012) Theory of Probability and its Applications, 56 (1), pp. 72-95. DOI: 10.1137/S0040585X97985200
Rokhlin, D.B. Lower bounds of martingale measure densities in the Dalang-Morton-Willinger theorem (2010) Theory of Probability and its Applications, 54 (3), pp. 447-465. DOI: 10.1137/S0040585X97984310
Rokhlin, D.B. On the existence of an equivalent supermartingale density for a fork-convex family of stochastic processes (2010) Mathematical Notes, 87 (3-4), pp. 556-563. DOI: 10.1134/S0001434610030338
Rokhlin, D.B. Equivalent supermartingale densities and measures in discrete time infinite horizon market models (2009) Theory of Probability and its Applications, 53 (4), pp. 626-647. DOI: 10.1137/S0040585X97983869
Rokhlin, D.B. The Kreps-Yan theorem for Banach ideal spaces (2009) Siberian Mathematical Journal, 50 (1), pp. 162-166. DOI: 10.1007/s11202-009-0018-3
Rokhlin, D.B. Constructive no-arbitrage criterion under transaction costs in the case of finite discrete time (2008) Theory of Probability and its Applications, 52 (1), pp. 93-107. DOI: 10.1137/S0040585X97982803
Rokhlin, D.B. Asymptotic arbitrage and numéraire portfolios in large financial markets (2008) Finance and Stochastics, 12 (2), pp. 173-194.
DOI: 10.1007/s00780-007-0056-2
Rokhlin, D.B. A theorem on martingale selection for relatively open convex set-valued random sequences (2007) Mathematical Notes, 81 (3-4), pp. 543-548.
DOI: 10.1134/S0001434607030315
Rokhlin, D.B. Martingale selection problem and asset pricing in finite discrete time (2007) Electronic Communications in Probability, 12, pp. 1-8.
DOI: 10.1214/ECP.v12-1240
Rokhlin, D.B. A martingale selection problem in the finite discrete-time case (2006) Theory of Probability and its Applications, 50 (3), pp. 420-435.
DOI: 10.1137/S0040585X97981834
Rokhlin, D., Schachermayer, W. A note on lower bounds of martingale measure densities (2006) Illinois Journal of Mathematics, 50 (4), pp. 815-824.
DOI: 10.1215/ijm/1258059493
Rokhlin, D.B. An extended version of the Dalang-Morton-Willinger theorem under portfolio constraints (2005) Theory of Probability and its Applications, 49 (3), pp. 429-443. DOI: 10.1137/S0040585X97981184
Rokhlin, D.B. The Kreps-Yan theorem for L^∞ (2005) International Journal of Mathematics and Mathematical Sciences, 2005 (17), pp. 2749-2756. DOI: 10.1155/IJMMS.2005.2749
Ipichev, V.G., Rokhlin, D.B., Ugol'Nitskii, G.A. On economic control mechanisms for bioresources (2000) Journal of Computer and Systems Sciences International, 39 (4), pp. 585-591.
Rokhlin, D.B. The asymptotic form of the spectrum of tidal Kelvin waves trapped by a boundary at large values of the Lamb parameter
(1999) Journal of Applied Mathematics and Mechanics, 63 (1), pp. 41-44. DOI: 10.1016/S0021-8928(99)00007-6
Rokhlin, D.B. On the spectral problem of the theory of tides in a bounded domain (1997) Doklady Akademii Nauk, 353 (5), pp. 619-621.
Potetyunko, E.N., Rokhlin, D.B. An asymptotic form of the fundamental solution of the perturbation propagation equation in an one-dimensional medium with low viscosity (1995) Prikladnaya Matematika i Mekhanika, 59 (2), pp. 336-339.
Talks at the international conferences
Bachelier's Third Colloquium on Financial Mathematics and Stochastic Analysis (Metabif, France, 2008)
Financial Mathematics Symposium: Methods and Applications (Gdansk, Poland, 2008)
International Conference "Stochastic Financial Mathematics" (Steklov Mathematical Institute, Moscow, 2013)
International conference "Nonlinear PPE and Financial Mathematics" (Germany, University of Applied Sciences, Zittau, 2015)
International conference "6th Russian-Armenian Workshop on Mathematical Analysis, Mathematical Physics and Analytical Mechanics" (2016, Rostov-on-Don)
Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis V-IX (2015-2019, Rostov-on-Don) International Scientific Workshop OTHA Fall 2020 (Rostov-on-Don, 2020)
II-V International conferences on stochastic methods (Divnomorskoe, 2017-2019, Moscow, online, 2020)
Other presentations
Vienna Technical University (Vienna, Austria, 2005),
University of Besancon (Besancon, France, 2008),
Big Seminar of the Department of Probability Theory, Moscow State University (Moscow, 2009),
CEMI seminar (Moscow, 2009), 6th School of Stochastics and Financial Mathematics (Sochi, 2015),
26th Crimean Autumn Mathematical School-Symposium (Laspi-Batiliman, 2015)
Academic degrees
1991 MSc in Applied Mathematics, Rostov State University
1998 Candidate of Physical and Mathematical Sciences, received in Saint-Petersburg State
University.
2010 Doctor of Physical and Mathematical Sciences, received in Steklov Mathematical
Institute of Russian Academy of Sciences
Current positions
Full Professor, Institute of Mathematics, Mechanics and Computer Sciences,
Southern Federal University
Leading Researcher of the Regional Scientific and Educational Mathematical Center of the Southern Federal University
Teaching:
