A model of rational choice among distributions of goal reaching times

Abstract

This research note develops a theory of rational choice among distributions of goal reaching times. A motivation of the choice problem considered here is the time optimal approach to portfolio selection by Burkhardt, which considers an investor who is interested to reach a predefined level of wealth and whose preferences can be defined on the feasible probability distributions of the time at which this goal is reached for the first time. Here a more general choice problem is considered, called time optimal decision making. The decision maker is faced with a set of mutually exclusive actions, each of which provides a known distribution of goal reaching times. It is shown that the axiomatic approach of rational choice of von Neumann/Morgenstern can be applied to reach again an expected utility representation for the preferences under consideration. This result not only provides a rational foundation for time optimal decision making, and particularly time optimal portfolio selection, but also for the analysis of time preferences in a stochastic setting, an approach which is completely new to the literature to the best of the author's knowledge. Prime areas of application are decision analysis, portfolio selection, the analysis of saving plans and the development of new financial products.