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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 22342.

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Date of creation: 26 Apr 2010
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Handle: RePEc:pra:mprapa:22342

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

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  1. Massa, Massimo & Simonov, Andrei, 2005. "Is learning a dimension of risk?," Journal of Banking & Finance, Elsevier, Elsevier, vol. 29(10), pages 2605-2632, October.
  2. Gerard Debreu, 1957. "Stochastic Choice and Cardinal Utility," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 39, Cowles Foundation for Research in Economics, Yale University.
  3. Steinbacher, Matjaz, 2008. "Stochastic Processes in Finance and Behavioral Finance," MPRA Paper 13603, University Library of Munich, Germany.
  4. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, Springer, vol. 5(4), pages 297-323, October.
  5. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, Econometric Society, vol. 66(3), pages 497-528, May.
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