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.