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 introduce a computational method for determining policies which optimises 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. We reduce the state space used in the dynamic programming in order to provide a solution which is feasible and has less computational requirements. Numerical examples and comparison with other risk‐sensitive approaches are discussed.