Too Risk-Averse for Prospect Theory?

Marc Oliver Rieger, Thuy Bui

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DOI: 10.4236/me.2011.24077                

Abstract

We observe that the standard variant of Prospect Theory cannot describe very risk-averse choices in simple lotteries. This makes it difficult to accommodate it with experimental data. Using an exponential value function can solve this problem and allows to cover the whole spectrum of risk-averse behavior. Further evidence in favor of the exponential value function comes from the evaluation of data from a large scale survey on preferences over lotteries where the exponential value function produces the best fits. The results enhance the understanding on what types of lotteries pose potential problems for the classical value function.

Keywords

Cumulative Prospect Theory, Decisions under risk, Risk-Aversion, Probability Weighting, Value Function

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	D. Kahneman and A. Tversky, “Prospect Theory: An Analysis of Decision under Risk,” Econometrica, Vol. 47, No. 2, 1979, pp. 263-291.
[2]	A. Tversky and D. Kahneman, “Advances in Pro- spect Theory: Cumulative representation of Uncertainty,” Journal of Risk and Uncertainty, Vol. 5, No. 4, 1992, pp. 297-323.
[3]	A. Bruhin, H. Fehr-Duda and T. Epper, “Risk and rationality: Uncovering Heterogeneity in Probability Distortion,” Econometrica, Vol. 78, No. 4, 2010, pp. 1375-1412.
[4]	E. de Giorgi, H. Levy and T. Hens, “Existence of CAPM Equilibria with Prospect Theory Preferences,” Preprint 157, Institute for Empirical Economics, University of Zurich, 2004. HHHHUdoi:10.2139/ssrn.420184U
[5]	M. O. Rieger and M. Wang, “Cumulative Prospect Theory and the St. Petersburg Paradox,” Economic Theory, Vol. 28, 2006, pp. 665-679. HHHHUdoi:10.1007/s00199-005-0641-6U
[6]	D. Prelec, “The Probability Weighting Function,” Econo- metrica, Vol. 66, 1998, pp. 497-527.
[7]	U. S. Karmarkar, “Subjectively Weighted Utility: A Descriptive Extension of the Expected Utility Model,” Organizational Behavior and Human Performance, Vol. 21, No. 1, 1978, pp. 61-72. Udoi:UHHHHU10.1016/0030-5073(78)90039-9U
[8]	O. R. Marc and M. Wang, “Prospect Theory for Continuous Distributions,” Journal of Risk and Uncertainty, Vol. 36, No. 1, 2008, pp. 83-102. HHHHUdoi:10.1007/s11166-007-9029-2U
[9]	V. K?bberling and P. P. Wakker, “An Index of Loss Aversion,” Journal of Economic Theory, Vol. 122, 2005, pp. 119-131.
[10]	V. Zakalmouline and S. Koekebakker, “A Generalization of the Mean-Variance Analysis,” SSRN Working Paper, 2008.
[11]	C. Camerer and T.-H. Ho, “Violations of the betweenness Axiom and Nonlinearity in Probability,” Journal of Risk and Uncertainty, Vol. 8, No. 2, 1994, pp. 167-196.
[12]	M. Birnbaum and A. Chavez, “Tests of Theories of Decision Making: Violations of Branch Independence and Distribution Independence,” Organizational Behavior and Human Decision Processes, Vol. 71, No. 2, 1997, pp. 161-194.
[13]	H. Stott, “Cumulative Prospect Theory’S Functional Menagerie,” Journal of Risk and Uncertainty, Vol. 32, No. 2, 2006, pp. 101-130. HHHHUdoi:10.1007/s11166-006-8289-6U
[14]	S. Blondel, “Testing Theories of Choice under Risk: Estimation of Individual Functionals,” Journal of Risk and Uncertainty, Vol. 24, No. 3, 2002, pp. 251-265. HHHHUdoi:10.1023/A:1015687502895U
[15]	M. Wang, M. O. Rieger and T. Hens, “An Internatioanl Survey on Time Discounting,” SSRN Working Paper, 2009.
[16]	A. Mas-Colell, M. D. Whinston and J. R. Green, “Microeconomic Theory,” Oxford University Press, Oxford, 1995.