Markov decision processes with recursive risk measures

In this paper, we consider risk-sensitive Markov Decision Processes (MDPs) with Borel state and action spaces unbounded cost under both finite infinite planning horizons. Our optimality criterion is based on the recursive application of static risk measures. This motivated by utilities in economic literature, has been studied before for entropic measure extended here to an axiomatic characterization suitable We derive a Bellman equation prove existence Markovian optimal policies. For horizon, model shown be contractive policy stationary. Moreover, establish connection distributionally robust MDPs, which provides global interpretation recursively defined objective function. Monotone models are particular.