Dynamic Programming Equations for MDPs with AVaR Criteria for Unbounded Costs

In this paper we derive dynamic programming equations to minimize the Average-Value-at-Risk (AVaR) of the possibly unbounded $L^{p}$-costs in finite and infinite horizon which is generated by a Markov Decision Process (MDP). We show that with state aggregation and by using the convex analytic formulation of the optimization problem we can solve the problem as in risk-neutral case. To our knowledge, this is the first work of deriving dynamic programming equations with $L^{p}$-unbounded costs via AVaR-operator.