Optimal strategy in a trading problem with stochastic prices

A stochastic, dynamic version of a one-commodity stock-exchange problem is considered. The market prices are described by a Markov chain. At the beginning of each period the decision maker knows the level of his inventory of a commodity and the present market price. Then he decides to buy or sell some amount of the commodity. The resulting amount is treated as the next period inventory. The capacity of the store and the amount of the purchase are limited. A linear holding cost is introduced. An optimal purchase-sell policy which minimizes expected cost is given.