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Dmitry Borisovich Rokhlin 

Professor

Institute of Mathematics, Mechanics, and Computer Science named after of I.I. Vorovich

E-mail:
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Degree: Doctor of Sciences

Personal page in Russian:
https://sfedu.ru/person/dbrohlin
Personal page in English:
https://sfedu.ru/en/person/dbrohlin

Research interests:

optimal control, decision making under uncertainty, mathematical finance

Teaching:

  • Optimization methods and operations research
    The course includes the problems of convex optimization, duality theory, smooth optimization problems, linear programming, multi-criteria problems, antagonistic games, network optimization, dynamic programming. We present the basic methods for analysis of optimization problems and related algortihms. The mastering of this material will allow the students, performing their own research in some subject area, to chose an adequate problem formulation and methods for its analysis and solution.
  • Stochastic analysis
    We present information, which are necesssary for construction and investigation of models, based on the use of diffusion processes: (a) Brownian motion, integral and Ito formula, stochastic differential equation; (b) the connections with partial differential equations: Feynmann-Kac formula, probabilistic representation of the solution of elliptic and parabolic equations; (c) analysis of concrete problems: calculation of option prices and optimal investment in the Black-Scholes model, optimal selling an asset.
  • Problems of optimal control
    The aim of the course is to present the formualtion and solution methods of the optimal control problems. We consider the Pontryagin maximum principle, various versions of the Bellman equation (discrete and continuous time, finite and infinite horizon, stochastic systems), concepts of controllability and observability. The course is of applied nature and is focused on the solution of concrete problems.
  • Stochastic optimal control and mathematical finance
    We consider the notions, which are necessary to qualitative and quantitative description of stochastic control systems, driven by Brownian motion (optimality principle, Hamilton-Jacobi-Bellman equations, viscosity solutions). The course is aimed at the development of skills in analyzing ofvarious problems on the base of a unified methodology and at the analysis of concrete problems (Merton's problem, optimization of dividends flow, optimal realization of American Put option). Numerical methods are also studied (monotone finite-difference schemes, convergence justification).

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