Controlled Markov chains with risk-sensitive criteria: Average cost, optimality equations, and optimal solutions
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.
scientific article; zbMATH DE number 1439904