Dynamic Pricing with Surging Demand (CSIAM Transactions on Applied Mathematics, 2024)
This paper considers the case of a firm’s dynamic pricing problem for a nonperishable product experiencing surging demand caused by rare events modelled bya marked point process. The firm aims to maximize its running revenue by selectingan 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 resultingintegro-differential Hamilton-Jacobi-Bellman (HJB) equation and prove that the valuefunction is its unique classical solution. We also establish structural properties for ourproblem and find that the optimal price always decreases with initial inventory levelin the absence of surging demand. However, with surging demand, we find that theoptimal price could increase rather than decrease at the initial inventory level.