Revenue optimization of risk-averse managers with atemporal utility

We examine a revenue management problem with random demands from an advance market and a spot market when the revenue manager is risk averse with an atemporal utility function. This article investigates the impact of the degree of risk aversion and the level of demand uncertainty on the manager's optimal capacity allocation. We first show that the optimal booking limit for the advance market is increasing in the degree of the manager's risk aversion. We then identify a general sufficient condition assuring that a risk-averse manager's optimal booking limit is monotone in the level of demand uncertainty measured by stochastic dominance. With normally distributed demands, we gain additional insights on the impact of demand uncertainty together with the manager's risk attitude through a mean-variance analysis. In particular, we demonstrate that there exists a threshold revenue ratio such that the optimal booking limit is increasing in the demand volatility measured by the standard deviation whenever the revenue ratio is above the threshold, which is 0.5 for a risk-neutral manager and is strictly less than 0.5 for a risk-averse manager.