Geodesic
Optimal risk control under functionally restricted disturbances
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 5 (2013) no. 1, pp. 74-103.

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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. 
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Dmitry A. Serkov. Optimal risk control under functionally restricted disturbances. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 5 (2013) no. 1, pp. 74-103. http://geodesic.mathdoc.fr/item/MGTA_2013_5_1_a4/

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