Optimal Sequential Investment Decisions Under Conditions of Uncertainty

Abstract

This paper presents a mathematical model of sequential investment behavior under conditions of uncertainty. The model addresses the problem of an investor with access to a limited pool of capital, who makes sequential decisions on long-lasting investments, under uncertainty as to the timing or the quality of future opportunities. We derive optimal investment strategies for the cases where the return from investment is a convex or concave function, we present closed form solutions for commonly adopted return functions, and we evaluate how the optimal investment behavior should change when changes occur in the environment, or the underlying probability distributions. In addition, we analyze three modifications of the problem. The results presented in this paper extend previous results on investment behavior for long-lasting (irreversible) decisions; in addition, some results are in accordance with existing ones from portfolio theory and/or search theory.