Controlled Markov chains with risk-sensitive criteria: Average cost, optimality equations, and optimal solutions. (English) Zbl 0953.93077

Cavazos-Cadena, Rolando; Fernández-Gaucherand, Emmanuel

Math. Methods Oper. Res. 49, No. 2, 299-324 (1999).

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)

MSC:

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

Keywords:

stochastic optimal control; discrete-time controlled Markov chain; risk sensitive; simultaneous Doeblin condition