Value-At-Risk Optimal Policies for Revenue Management Problems

Consider a single-leg dynamic revenue management problem with fare classes controlled by capacity in a risk-averse setting. The revenue management strategy aims at limiting the down-side risk, and in particular, value-at-risk. A value-at-risk optimised policy offers an advantage when considering applications which do not allow for a large number of reiterations. They allow for specifying a confidence level regarding undesired scenarios. We state the underlying problem as a Markov decision process and provide a computational method for computing policies, which optimise the value-at-risk for a given confidence level. This is achieved by computing dynamic programming solutions for a set of target revenue values and combining the solutions in order to attain the requested multi-stage risk-averse policy. Numerical examples and comparison with other risk-sensitive approaches are discussed.