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Average optimality for risk-sensitive control with general state space

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  • Anna Ja'skiewicz

Abstract

This paper deals with discrete-time Markov control processes on a general state space. A long-run risk-sensitive average cost criterion is used as a performance measure. The one-step cost function is nonnegative and possibly unbounded. Using the vanishing discount factor approach, the optimality inequality and an optimal stationary strategy for the decision maker are established.

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  • Anna Ja'skiewicz, 2007. "Average optimality for risk-sensitive control with general state space," Papers 0704.0394, arXiv.org.
    • Handle: RePEc:arx:papers:0704.0394
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    1. Balaji, S. & Meyn, S. P., 2000. "Multiplicative ergodicity and large deviations for an irreducible Markov chain," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 123-144, November.
    2. Manfred Schäl, 1993. "Average Optimality in Dynamic Programming with General State Space," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 163-172, February.
    3. V. S. Borkar & S. P. Meyn, 2002. "Risk-Sensitive Optimal Control for Markov Decision Processes with Monotone Cost," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 192-209, February.
    4. Tomasz Bielecki & Daniel Hernández-Hernández & Stanley R. Pliska, 1999. "Risk sensitive control of finite state Markov chains in discrete time, with applications to portfolio management," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 167-188, October.
    5. Lukasz Stettner, 1999. "Risk sensitive portfolio optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(3), pages 463-474, December.
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