Stopping rules for utility functions and the St. Petersburg gamble

We study, using the St. Petersburg paradox, the risk attitudes expressed by utility functions without the normal continuity and differentiability assu mptions. We model the repeated St. Petersburg lottery with two parameters, starting wealth and return ratio, as a stochastic process with a simple con trol mechanism and the objective of maximizing utility of the outcome. A st opping function expresses the earliest stopping stage; a finite value resol ves the paradox. This new approach can measure the risk attitude of discont inuous utilities in only a finite horizon repetition of the lottery, openin g the door to new usefulness of the utility concept in modeling. As an Exam ple we give an application to behavior of persons receiving entitlements to wards additional income from working. (C) 1999 Elsevier Science Inc. All ri ghts reserved.