Center for Risk Management Research

We consider a ¯rm facing random demand at the end of a single period of random length. At any time during the period, the ¯rm can either increase or decrease inventory by buying or selling on a spot market where price °uctuates randomly over time, and the revenue the ¯rm gets by meeting demand at the end of the period is a function of the spot market price at that time. We ¯rst demonstrate that this control problem is equivalent to a singular control problem of higher dimensions. We then use this insight combined with a novel control-theoretic approach to show that the optimal policy is completely characterized by a simple price-dependent two threshold policy. In a series of computational experiments, we explore the value of actively managing inventory during the period rather than making a purchase decision at the start of the period,and then waiting for demand.