Norwegian-Ukrainian Winter School 2018 on Stochastic Analysis, Probability Theory and Related Topics Abstracts of the presentations
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چکیده
We give a short introduction to the stochastic calculus for Itô-Lévy processes, and review briey the two main methods of optimal control of stochastic systems described by such processes, namely: (i) Dynamic programming and the Hamilton-Jacobi-Bellman (HJB) equation (ii) The stochastic maximum principle and its associated adjoint backward stochastic di¤erential equation (BSDE). The two methods are illustrated by application to the classical portfolio optimization problem in nance. A second application is the problem of risk minimization in a nancial market. Using a dual representation of risk, we arrive at a stochastic di¤erential game. This is solved by using the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation, which is an extension of the HJB equation to stochastic di¤erential games. Professor Andriy Pylypenko, Institute of Mathematics, National Academy of Science of Ukraine, Kiev, Ukraine Title: "The limit behavior of perturbed random walks"
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