Value-at-risk optimal policies for revenue management problems

Abstract

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.

A review of revenue management: Recent generalizations and advances in industry applications

“…Not only in finance, risk measures are receiving more and more attention. Koenig and Meissner (2015a) and Koenig and Meissner (2015b) consider the optimization of the risk measures "target percentile risk" and "value-at-risk", respectively. In the language of RM, the target percentile risk expresses the probability that a certain target value of revenue is not exceeded, while the value-at-risk evaluates the revenue that will not be exceeded at a given probability level.…”

“…Note that most literature focuses on a certain objective criterion and theoretically analyses toy settings. However, there is also some literature without clear objective, but where risk-neutral approaches are slightly modified by calibrateable parameters such that expected utility or an arbitrary risk measure can be optimized on demand, either manually Chang 2011 andMeissner 2015b) or by simulation-based optimization (Koch et al 2016).…”

Resilient revenue management: a literature survey of recent theoretical advances

“…Alternatively, it can be useful to limit the acceptable risk in the mathematical model explicitly. Risk plays a particularly significant role for smaller sales industries, such as event promotion, which can only afford low levels of risk (Koenig and Meissner, 2015).…”

“…Revenue risk is also measured in terms of value-at-risk or conditional-value-atrisk in Koenig and Meissner (2015a), Koenig and Meissner (2015b), Gönsch and Hassler (2013), and Koenig and Meissner (2015). In contrast, Lancaster (2003) recommends relative risk measures and proposes a revenue-per-available-seat-mile indicator.…”

A multi-objective approach for PH-graphs with applications to stochastic shortest paths

“…Related work SSPPs are considered in many different applications ranging from transportation (Barbarosoǧlu and Arda 2004;Nikolova and Karger 2008) to computer networks (Nain and Towsley 2016), data migration (Li et al 2016), social networks (Rezvanian and Reza Meybodi 2016) or finance (Budd 2016;Koenig and Meissner 2015). An enormous number of papers has been published in the area such that we can only highlight a few, most relevant results for our work.…”