Optimal dynamic pricing of inventories with stochastic demand and discounted criterion

We consider a continuous time dynamic pricing problem for selling a given number of items over a finite or infinite time horizon. The demand is price sensitive and follows a non-homogeneous Poisson process. We formulate this problem as to maximize the expected discounted revenue and obtain the structural properties of the optimal revenue function and optimal price policy by the Hamilton–Jacobi–Bellman (HJB) equation. Moreover, we study the impact of the discount rate on the optimal revenue function and the optimal price. Further, we extend the problem to the case with discounting and time-varying demand, the infinite time horizon problem. Numerical examples are used to illustrate our analytical results.

► We consider a continuous time dynamic pricing problem under discounted criterion.
► A new method is proposed to analysis the HJB equation of the optimal function.
► The relationship of the optimal policy with state variables is fully investigated.
► The model is extended by considering time varying demand and discount rate.
► The infinite time horizon problem is also analyzed.