Markov decision processes with recursive risk measures

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 equa-tion 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 num-ber 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. (c) 2021 Elsevier B.V. All rights reserved.