Decomposing risk in an exploitation–exploration problem with endogenous termination time

Abstract

An expected utility risk averse maximizer must decide on an investment policy for a set of N projects. The budget for investment is fixed and it is allocated to the projects gradually over time by an endogenously determined amount. We allow for simultaneous investments in different projects as well as investments in the same project at different times. The termination time is endogenous. The problem finishes, at latest, when the budget is fully depleted. Our problem has an exploitation versus exploration trade off. There are unknown relevant characteristics of each project that the decision maker only learns by investing in the corresponding project. We analyze the performance of dynamic programming based policies. Particularly, we use differences in the value functions of N single-project problems to construct the opportunity cost of investing in each project. Those opportunity costs drive the investment policy for the N project problem.