Dynamic Risk Measures for Finite-State Partially Observable Markov Decision Problems

Abstract

In this paper, we provide a theory of time-consistent dynamic risk measures for finite-state partially observable Markov decision problems. By employing our new concept of stochastic conditional time consistency, we show that such dynamic risk measures have a special structure, given by transition risk mappings as risk measures on the space of functionals on the observable state space only. Moreover, these mappings enjoy a strong monotonicity with respect to first order stochastic dominance.