How to Solve the St Petersburg Paradox in Rank-Dependent Models?

Abstract

The Cumulative Prospect Theory, as it was specified by Tversky and Kahneman (1992) does not explain the St Petersburg Paradox. This study shows that the solutions proposed in the literature (Blavatskyy, 2005; Rieger and Wang, 2006) to guarantee, under rank dependent models, finite subjective utilities for any prospects with finite expected values, have to cope with many limitations. In that framework, CPT fails to accommodate both gambling and insurance behavior. We suggest replacing the weighting function generally proposed in the literature by another specification which respects the following properties: 1) In order to guarantee finite subjective values for all prospects with finite expected values, the slope at zero has to be finite. 2) To account for the fourfold pattern of risk attitudes, the probability weighting has to be strong enough to overcome the concavity of the value function.

Keywords: St Petersburg Paradox, Cumulative Prospect Theory, Gambling, Probability Weighting

JEL Classification: D81, C91