The (S,s) Policy is an Optimal Trading Strategy in a Class of Commodity Price Speculation Problems

This paper introduces a model of commodity price speculation and proves that the optimal trading strategy is of the (S,s) form when a no expected loss condition holds. A strong form of this condition is that the retail price charged to consumers at time t exceeds the expected wholesale price of the commodity at time t+1, i.e. , where β ∈(0,1) is the speculator’s discount factor. We are extremely grateful to Herbert Scarf for pointing out an important error in a previous draft of this paper and for suggesting the key argument in a revised proof that fixed the problem. We also benefited from helpful feedback from an anonymous referee, William Brainard, Zvi Eckstein, participants of seminars at Yale, the Operations Research Center at MIT, and the Econometric Society Winter School at the Indian Statistical Institute, New Delhi.