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Commutative Prospect Theory and Stopped Behavioral Processes for Fair Gambles

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  • Cadogan, Godfrey

Abstract

We augment Tversky and Khaneman (1992) (“TK92”) Cumulative Prospect Theory (“CPT”) function space with a sample space for “states of nature”, and depict a commutative map of behavior on the augmented space. In particular, we use a homotopy lifting property to mimic behavioral stochastic processes arising from deformation of stochastic choice into outcome. A psychological distance metric (in the class of Dudley-Talagrand inequalities) popularized by Norman (1968); Nosofsky and Palmeri (1997), for stochastic learning, was used to characterize stopping times for behavioral processes. In which case, for a class of nonseparable space-time probability density functions, based on psychological distance, and independently proposed by Baucells and Heukamp (2009), we find that behavioral processes are uniformly stopped before the goal of fair gamble is attained. Further, we find that when faced with a fair gamble, agents exhibit submartingale [supermartingale] behavior, subjectively, under CPT probability weighting scheme. We show that even when agents’ have classic von Neuman-Morgenstern preferences over probability distribution, and know that the gamble is a martingale, they exhibit probability weighting to compensate for probability leakage arising from the their stopped behavioral process.

Suggested Citation

  • Cadogan, Godfrey, 2010. "Commutative Prospect Theory and Stopped Behavioral Processes for Fair Gambles," MPRA Paper 22342, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:22342
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    References listed on IDEAS

    as
    1. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    2. Massa, Massimo & Simonov, Andrei, 2005. "Is learning a dimension of risk?," Journal of Banking & Finance, Elsevier, vol. 29(10), pages 2605-2632, October.
    3. Gerard Debreu, 1957. "Stochastic Choice and Cardinal Utility," Cowles Foundation Discussion Papers 39, Cowles Foundation for Research in Economics, Yale University.
    4. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    5. Steinbacher, Matjaz, 2008. "Stochastic Processes in Finance and Behavioral Finance," MPRA Paper 13603, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    commutative prospect theory; homotopy; stopping time; behavioral stochastic process;

    JEL classification:

    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • C0 - Mathematical and Quantitative Methods - - General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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