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In classical Markov Decision Processes (MDPs), action costs and transitionprobabilities are assumed to be known, although an accurate estimation of theseparameters is often not possible in practice. This study addresses MDPs undercost and transition probability uncertainty and aims to provide a mathematicalframework to obtain policies minimizing the risk of high long-term losses dueto not knowing the true system parameters. To this end, we utilize the riskmeasure value-at-risk associated with the expected performance of an MDP modelwith respect to parameter uncertainty. We provide mixed-integer linear andnonlinear programming formulations and heuristic algorithms for suchrisk-averse models of MDPs under a finite distribution of the uncertainparameters. Our proposed models and solution methods are illustrated on aninventory management problem for humanitarian relief operations during aslow-onset disaster. The results demonstrate the potential of our risk-aversemodeling approach for reducing the risk of highly undesirable outcomes inuncertain/risky environments.

Risk Aversion to Parameter Uncertainty in Markov Decision Processes with an Application to Slow-Onset Disaster Relief