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Existence of risk-sensitive optimal stationary policies for controlled Markov processes. (English) Zbl 0937.90115
Summary: The authors are concerned with the existence of optimal stationary policies for infinite-horizon risk-sensitive Markov control processes with denumerable state space, unbounded cost function, and long-run average cost. Introducing a discounted cost dynamic game, they prove that its value function satisfies an Isaacs equation, and its relationship with the risk-sensitive control problem is studied. Using the vanishing discount approach, they prove that the risk-sensitive dynamic programming inequality holds, and derive an optimal stationary policy.

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