Solution to the risk-sensitive average cost optimality equation in a class of Markov decision processes with finite state space

Rolando Cavazos-Cadena

Mathematical Methods of Operations Research, 2003, vol. 57, issue 2, 263-285

Abstract: This work concerns discrete-time Markov decision processes with finite state space and bounded costs per stage. The decision maker ranks random costs via the expectation of the utility function associated to a constant risk sensitivity coefficient, and the performance of a control policy is measured by the corresponding (long-run) risk-sensitive average cost criterion. The main structural restriction on the system is the following communication assumption: For every pair of states x and y, there exists a policy π, possibly depending on x and y, such that when the system evolves under π starting at x, the probability of reaching y is positive. Within this framework, the paper establishes the existence of solutions to the optimality equation whenever the constant risk sensitivity coefficient does not exceed certain positive value. Copyright Springer-Verlag Berlin Heidelberg 2003

Keywords: AMS Subject Classifications: Primary, 90C40, 93E20; Secondary, 60J05, Key words: Exponential utility function, Constant risk sensitivity, Constant average cost, Weak communication condition, Contractive Operator, (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/s001860200256

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