 Markov decision processes with recursive risk measuresNicole Bäuerle and Alexander Glauner European Journal of Operational Research, 2022, vol. 296, issue 3, 953-966 Abstract: In this paper, we consider risk-sensitive Markov Decision Processes (MDPs) with Borel state and action spaces and unbounded cost. We treat both finite and infinite planning horizons. Our optimality criterion is based on the recursive application of static risk measures. This is motivated by recursive utilities in the economic literature. It has been studied before for the entropic risk measure and is extended here to general static risk measures. Under direct assumptions on the model data we derive a Bellman equation and prove the existence of optimal Markov policies. For an infinite planning horizon, the model is shown to be contractive and the optimal policy to be stationary. Our approach unifies results for a number of well-known risk measures. Moreover, we establish a connection to distributionally robust MDPs, which provides a global interpretation of the recursively defined objective function. Monotone models are studied in particular. Keywords: Dynamic programming; Risk-sensitive Markov decision process; Risk measure; Robustness (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:296:y:2022:i:3:p:953-966 DOI: 10.1016/j.ejor.2021.04.030 Access Statistics for this article European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati More articles in European Journal of Operational Research from Elsevier |
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