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Risk-sensitive control of discrete-time Markov processes with infinite horizon. (English) Zbl 0946.93043
This paper deals with infinite horizon risk sensitive control problems of discrete time Markov processes. Using three different approaches, i.e. (i) span-norm contraction (ii) discounted exponential cost criterion approximation (iii) stochastic discounted game approach, the authors obtain the solution to the Bellman equation corresponding to risk sensitive ergodic control, under different assumptions. Moreover, they investigate the asymptotic behavior for a vanishing risk factor and show that in the limit it reaches the optimal value for an average cost per unit time.
Reviewer: M.Nisio (Osaka)

MSC:
93E20 Optimal stochastic control
60J05 Discrete-time Markov processes on general state spaces
93C55 Discrete-time control/observation systems
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