Constrained Risk-Sensitive Markov Decision Chains

Karel Sladký

Chapter 59 in Operations Research Proceedings 2008, 2009, pp 363-368 from Springer

Abstract: Summary We consider a Markov decision chain $${X = \{ X_n ,n = 0,1 \cdots \}}$$ with finite state space I = {1; 2;…;N} and finite set A i = {1; 2;…;K i} of possible decisions (actions) in state i Є I. posing that in state i Є I action a ЄA i is selected, then state j is reached in the next transition with a given probability p ij (a) and one-stage transition rewards r ij (a) and s ij (a) will be accrued to such transition. We shall suppose that the streams of transition rewards are evaluated by an exponential utility function, say $${u^\gamma ( \cdot )}$$ , with risk aversion coefficient γ 0 (the risk seeking case). Then the utility assigned to the (random) reward ξ is given by $${u^{\rm \gamma } (\xi ): = {\rm sign (\gamma ) exp (\gamma \xi )}}$$ .

Date: 2009
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DOI: 10.1007/978-3-642-00142-0_59

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