Optimal risk control under functionally restricted disturbances
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 5 (2013) no. 1, pp. 74-103
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@article{MGTA_2013_5_1_a4,
author = {Dmitry A. Serkov},
title = {Optimal risk control under functionally restricted disturbances},
journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
pages = {74--103},
publisher = {mathdoc},
volume = {5},
number = {1},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MGTA_2013_5_1_a4/}
}
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/