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Controlled Markov chains with risk-sensitive criteria: Average cost, optimality equations, and optimal solutions. (English) Zbl 0953.93077
This paper deals with control problems of a discrete-time controlled Markov chain with denumerable state space. Endowing a risk sensitive average cost criterion, the authors obtained the following results, under a simultaneous Doeblin condition. If the risk sensitive coefficient is small enough, then the associated optimality equation has a bounded solution yielding a constant optimal cost. Moreover an optimal stationary policy is given, whenever a continuity-compact condition is satisfied.
Reviewer: M.Nisio (Osaka)

93E20 Optimal stochastic control
90C40 Markov and semi-Markov decision processes