A stochastic dynamic pricing and advertising model under risk aversion

This article analyzes a dynamic pricing and advertising model for the sale of perishable products under constant absolute risk aversion. We consider a time-dependent version of Gallego and van Ryzin's dynamic pricing model with exponential demand and include isoelastic advertising effects as well as marginal unit costs. We derive closed-form expressions of the optimal risk-averse pricing and advertising policies of the value function and of the certainty equivalent. The formulas provide insight into the (complex) interplay between risk-sensitive pricing and advertising decisions. Moreover, to evaluate the optimally controlled sales process over time we propose efficient simulation techniques. These are used to analyze the characteristics of different degrees of risk aversion, particularly the concentration of the profit distribution and the impact on the expected evolution of price and advertising rates.