On the notions and properties of risk and risk aversion in the time optimal approach to decision making

Abstract

This research proposes and discusses proper notions of risk and risk aversion for risks in the dimension of time, which are suitable for the analysis of time optimal decision making according to Burkhardt. The time optimal approach assumes a decision maker with a given goal, e.g. a given future wealth level, that he would like to reach as early as possible. To reach the goal, he can choose from a set of mutually exclusive actions, e.g. risky investments, for which the respective probability distributions of the goal reaching times are known. Our notions of risk and risk aversion are new and derived based on a rational model of choice. They yield intuitively appealing results which are exemplified by an application to an insurance problem. Furthermore, we investigate the choice implications of positive, zero, and negative risk aversion by means of a new St. Petersburg Game. The results indicate that in the time optimal approach nonnegative risk aversion would generally result in counterintuitive choices, whereas negative risk aversion shows the potential to imply plausible choices.