Stopping rules for utility functions and the St. Petersburg gamble

Abstract

We study, using the St. Petersburg paradox, the risk attitudes expressed by utility functions without the normal continuity and differentiability assumptions. We model the repeated St. Petersburg lottery with two parameters, starting wealth and return ratio, as a stochastic process with a simple control mechanism and the objective of maximizing utility of the outcome. A stopping function expresses the earliest stopping stage; a finite value resolves the paradox. This new approach can measure the risk attitude of discontinuous utilities in only a finite horizon repetition of the lottery, opening the door to new usefulness of the utility concept in modeling. As an Example we give an application to behavior of persons receiving entitlements towards additional income from working.