Optimal risk control under functionally restricted disturbances

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.