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Numeric solutions of worst-case optimal hedging and optimal selection problems

Priority areas of development: economics
2016
The project has been carried out as part of the HSE Program of Fundamental Studies.

Goal of research: A comprehensive analysis of portfolio selection problem within a guaranteed (worst-case) approach in real-world market, and a study of it numeric solutions.

Methodology:  Stochastic dynamic programming, convex analysis, linear programming, numerical methods and data visualization based on cutting-edge research papers. Numerical computations were carried out using the Matlab software.

Empirical base of research: Daily trading data from the Equities sector of Moscow exchange: close prices, last buy/sell prices,  min/max prices, average prices, trading volumes.

Results of research: We build a probabilistic framework for a guaranteed (worst-case) approach to controlling a general stochastic system. Within this framework we obtain a Bellman-Isaacs equation and a verification theorem. Applying this approach to the optimal investment problem we obtain sufficient conditions for concavity of the value function in presence of trading limits and transaction costs represented by a general function. We present a numerical procedure for finding a solution to this problem and provided sufficient conditions for the value function being bounded and finite in the portfolio management problem in a general setting.  We also justify that the developed approach is applicable as a decision support system within an investment management process.

Publications:


Andreev N. A. Boundedness of the value function of the worst-case portfolio selection problem with linear constraints / NRU Higher School of Economics. Series FE "Financial Economics". 2017. No. WP BRP 59/FE/2017.
Андреев Н. А., Смирнов С. Н. Гарантированный подход к задачам инвестирования и хеджирования // В кн.: "Тихоновские чтения": научная конференция: тезисы докладов: посвящается памяти академика Андрея Николаевича Тихонова: 29 октября-2 ноября 2018 г. М. : МАКС Пресс, 2018. С. 11-11.