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. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p^r_t \ge \beta E\{p_{t+1}|p_t,x_t\}$$\end{document}, where β ∈(0,1) is the speculator’s discount factor.