Solving the St. Petersburg Paradox in cumulative prospect theory: the right amount of probability weighting

Theory and Decision 71 (3):325-341 (2011)
Abstract
Cumulative Prospect Theory (CPT) does not explain the St. Petersburg Paradox. We show that the solutions related to probability weighting proposed to solve this paradox, (Blavatskyy, Management Science 51:677–678, 2005; Rieger and Wang, Economic Theory 28:665–679, 2006) have to cope with limitations. In that framework, CPT fails to accommodate both gambling and insurance behavior. We suggest replacing the weighting functions generally proposed in the literature by another specification which respects the following properties: (1) to solve the paradox, 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.
Keywords St. Petersburg Paradox  Cumulative prospect theory  Gambling  Probability weighting
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