An Optimal Stopping Problem of a Growing Inventory

This paper deals with the problem of explaining the behavior of a producer entering the period with growing inventory, while the current price and a stochastic distribution of prices for the following period are given. The conceptual framework is one of searching for an optimal stopping rule for this problem. It is shown that the optimal policy consists of finding a unique cutoff price function, which is non-increasing with respect to the age of the stock.