Article

Markov Decision Processes with Average-Value-at-Risk criteria

Mathematical Methods of Operational Research (Impact Factor: 0.31). 12/2011; 74(3):361-379. DOI: 10.1007/s00186-011-0367-0

ABSTRACT We investigate the problem of minimizing the Average-Value-at-Risk (AVaR

τ
) 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 AVaR

τ
. 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 AVaR

τ
-criterion.

KeywordsMarkov Decision Problem–Average-Value-at-Risk–Time-consistency–Risk aversion

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