Dynamic Pricing With Customer Purchase Postponement

We consider a dynamic pricing model for a firm that sells perishable products to customers who have the potential to postpone the purchase decision to reduce their perceived risk. The firm has a competitor in the market and knows that the competitor adopts a static pricing strategy. We assume that the customer arrivals follow a stochastic differential equation with delay and establish a continuous-time model so as to maximize the expected profit. When the probability distribution of the customers’ reservation value is exponential and its parameter is constant in time, a closed-form optimal pricing policy is obtained. Then, we show the impact of the competitor's pricing policy on the optimal price sample path through a martingale approach. Moreover, we show that the purchasing postponement reduces the firm’s total expected profit.