Dynamic Pricing with Stochastic Reference Price Effect

We study a dynamic pricing problem of a firm facing stochastic reference price effect. Randomness is incorporated in the formation of reference prices to capture either consumers’ heterogeneity or exogenous factors that affect consumers’ memory processes. We apply the stochastic optimal control theory to the problem and derive an explicit expression for the optimal pricing strategy. The explicit expression allows us to obtain the distribution of the steady-state reference price. We compare the expected steady-state reference price to the steady-state reference price in a model with deterministic reference price effect, and we find that the former one is always higher. Our numerical study shows that the two steady-state reference prices can have opposite sensitivity to the problem parameters and the relative difference between the two can be very significant.