Abstract. P We investigate the problem of minimizing the Average-Value-at-Risk (AV aRτ ) of the discounted cost over a finite and an infinite horizon which is generated by a Markov Decision Process (MDP). We show that this problem can be reduced to an ordinary MDP with extended state space and give conditions under which an optimal policy exists. We also give a time-consistent interpretation of the AV aRτ . At the end we consider a numerical example which is a simple repeated casino game. It is used to discuss the influence of the risk aversion parameter τ of the AV aRτ -criterion.
In REF the authors address the problem of minimizing the AVaR of the discounted cost over a finite and an infinite horizon, and propose a dynamic programming approach based on state augmentation.
Markov Decision Processes with Average-Value-at-Risk criteria
Mathematical Methods of Operations Research
Computer Science Mathematics