  In this paper, we consider risk-sensitive Markov Decision Processes (MDPs)
with Borel state and action spaces and unbounded cost under 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, has been studied before for the entropic risk
measure and is extended here to an axiomatic characterization of suitable risk
measures. We derive a Bellman equation and prove the existence of Markovian
optimal policies. For an infinite planning horizon, the model is shown to be
contractive and the optimal policy to be stationary. 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.
