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Bounded cumulative prospect theory: some implications for gambling outcomes

Author

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  • Michael Cain
  • David Law
  • David Peel

Abstract

Standard parametric specifications of Cumulative Prospect theory (CPT) can explain why agents bet on longshots at actuarially unfair odds. However, the standard specification of CPT cannot explain why people might bet on more favoured outcomes, where by construction the greatest volume of money is bet. This article outlines a parametric specification than can consistently explain gambling over all outcomes. In particular we assume that the value function is bounded from above and below and that the degree of loss aversion experienced by the agent is smaller for small-stake gambles (as a proportion of wealth) than usually assumed in CPT. There are a number of new implications of this specification. Boundedness of the value function in CPT implies that the indifference curve between expected-return and win-probability for a given stake will typically exhibit both an asymptote (implying rejection of an infinite gain bet) and a minimum, as the shape of the value function dominates the probability weighting function. Also the high probability section of the indifference curve will exhibit a maximum.

Suggested Citation

  • Michael Cain & David Law & David Peel, 2008. "Bounded cumulative prospect theory: some implications for gambling outcomes," Applied Economics, Taylor & Francis Journals, vol. 40(1), pages 5-15.
    • Handle: RePEc:taf:applec:v:40:y:2008:i:1:p:5-15
    DOI: 10.1080/00036840701728765
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    References listed on IDEAS

    as
    1. Gilbert W. Bassett, Jr., 1987. "The St. Petersburg Paradox and Bounded Utility," History of Political Economy, Duke University Press, vol. 19(4), pages 517-523, Winter.
    2. repec:ebl:ecbull:v:4:y:2007:i:26:p:1-10 is not listed on IDEAS
    3. Charles T. Clotfelter & Philip J. Cook, 1989. "Selling Hope: State Lotteries in America," NBER Books, National Bureau of Economic Research, Inc, number clot89-1, July.
    4. David Peel & David Law, 2007. "Betting on odds on Favorites as an Optimal Choice in Cumulative Prospect Theory," Economics Bulletin, AccessEcon, vol. 4(26), pages 1-10.
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    1. David Peel & David Law, 2009. "A More General Non‐expected Utility Model as an Explanation of Gambling Outcomes for Individuals and Markets," Economica, London School of Economics and Political Science, vol. 76(302), pages 251-263, April.
    2. Mao-Wei Hung & Jr-Yan Wang, 2011. "Loss aversion and the term structure of interest rates," Applied Economics, Taylor & Francis Journals, vol. 43(29), pages 4623-4640.
    3. David Alan Peel & David Law, 2017. "Loss Aversion And Ruinous Optimal Wagers In Cumulative Prospect Theory," Economics Bulletin, AccessEcon, vol. 37(1), pages 352-360.
    4. Peel, D.A. & Zhang, Jie, 2009. "The expo-power value function as a candidate for the work-horse specification in parametric versions of cumulative prospect theory," Economics Letters, Elsevier, vol. 105(3), pages 326-329, December.
    5. David A. Peel & Davind Law, 2009. "An Explanation of Optimal Each-Way Bets based on Non-Expected Utility Theory," Journal of Gambling Business and Economics, University of Buckingham Press, vol. 3(2), pages 15-35, September.

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