Controlled Markov Decision Processes with AVaR criteria for unbounded costs

In this paper, we consider the control problem with the Average-Value-at-Risk (AVaR) criteria of the possibly unbounded L1-costs in infinite horizon on a Markov Decision Process (MDP). With a suitable state aggregation and by choosing a priori a global variable s heuristically, we show that there exist optimal policies for the infinite horizon problem for possibly unbounded costs.