Risk in Revenue Management and Dynamic Pricing

We present a new model for optimal dynamic pricing of perishable services or products that incorporates a simple risk measure permitting control of the probability that total revenues fall below a minimum acceptable level. The formulation assumes that sales must occur within a finite time period, that there is a finite—possibly large—set of available prices, and that demand follows a price-dependent, nonhomogeneous Poisson process. This model is particularly appropriate for applications in which attainment of a revenue target is an important consideration for managers; for example, in event management, in seasonal clearance of high-value items, or for business subunits operating under performance targets. We formulate the model as a continuous-time optimal control problem, obtain optimality conditions, explore structural properties of the solution, and report numerical results on problems of realistic size.