A dual control approach to optimal pricing

The optimal pricing policy of a monopolistic firm facing random demand and maximizing its expected profit over a period of several stages is considered. The demand function is assumed to be time invariant but unknown. A special case when the cost is certain and the demand is a linear function of the price is investigated. This is formulated as a stochastic control problem. It is found that when both the intercept and slope of the demand function are unknown, the optimal pricing policy does not correspond to optimal prices for each individual stage. Approximate methods are used to find the optimal policies. Simulation results are given.