Controlled Markov Chains with AVaR Criteria for Unbounded Costs

Abstract

In this paper, we consider the control problem with the Average-Value-at-Risk (AVaR) criteria of the possibly unbounded $L^1$-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. To our knowledge, this is the first work of deriving dynamic programming equations with $L^1$-unbounded costs via AVaR-operator.

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