This article is cited in 4 papers

Optimal risk control under functionally restricted disturbances

Dmitry A. Serkov<sup>ab

a</sup> Institute of Mathematics and Mechanics named after N. N. Krasovskii, Ural Branch of Russian Academy of Sciences
^b Ural Federal University named after the first President of Russia B. N. Yeltsin

Abstract: We study the optimal risk and how to build the strategy optimal for risk in cases where disturbance is constrained by some unknown functional limitation of a certain family. It is shown that for a class of controlled systems, the problem is solvable in the class of strategies with full memory; the optimal risk coincides with the optimal risk in the class quasi-strategy. The description of the optimal risk and the risk-optimal strategies based on the programmed iterations of the regret functional are provided. Examples of a risk-optimal strategy, cases and conditions of degeneration of the iterative process are given.

Keywords: strategy with full memory, Savage criterion, functionally limited disturbance, quasi-strategy, the method of program iterations.

UDC: 517.952+517.977
BBK: 22.18