Dynamic Pricing with Surging Demand

This paper considers the case of a firm’s dynamic pricing problem for a nonperishable product experiencing surging demand caused by rare events modelled by a marked point process. The firm aims to maximize its running revenue by selecting an optimal price process for the product until its inventory is depleted. Using the dynamic program and inspired by the viscosity solution technique, we solve the resulting integro-differential Hamilton-Jacobi-Bellman (HJB) equation and prove that the value function is its unique classical solution. We also establish structural properties for our problem and find that the optimal price always decreases with initial inventory level in the absence of surging demand. However, with surging demand, we find that the optimal price could increase rather than decrease at the initial inventory level.