Using Fuzzy Probability Weights in Cumulative Prospect Theory
Abstract
During the past years, a rapid growth has been seen in the descriptive approaches to decision choice. As opposed to normative expected utility theory, these approaches are based on the subjective perception of probabilities by the individuals, which takes place in real situations of risky choice. The modelling of this kind of perceptions is made on the basis of probability weighting functions. In cumulative prospect theory, which is the focus of this paper, decision prospect outcome weights are calculated using the obtained probability weights. If the value functions are constructed in the sets of positive and negative outcomes, then, based on the outcome value evaluations and outcome decision weights, generalised evaluations of prospect value are calculated, which are the basis for choosing an optimal prospect. In cumulative prospect theory, all relevant evaluations are represented in deterministic form. The present research is an attempt to extend classical prospect theory to the cases when the weights of probabilities are given in a fuzzy form.
Keywords: |
Fuzzy probability weight; probability weighting function; prospect theory; utility theory
|
Full Text: |
References
A. Tversky and D. Kahneman, “Advances in prospect theory: cumulative representation of uncertainty,” Journal of Risk and Uncertainty, vol. 5, issue 4, pp. 297–327, Oct. 1992. https://doi.org/10.1007/BF00122574
J. von Neuman and O. Morgenstern. Theory of Games and Economic Behavior, Princeton University Press, 1944.
W. Edwards, “The Theory of Decision Making,” Psychological Bulletin, vol. 51, no. 4, pp. 380–417, 1954. https://doi.org/10.1037/h0053870
W. Edwards, “Subjective Probabilities Inferred from Decisions,” Psychological Review, vol. 69, pp. 109–135, 1962.
M. Allais, “Le comportement de l′homme rationell devant le risqué: Critique des postulats et axioms de l′école américaine”. Econometrica, vol. 21, pp. 503–546, 1953. https://doi.org/10.2307/1907921
M. J. Machina, “Choice under Uncertainty: Problems Solved and Unsolved,” Perspectives, vol. 1, no. 1, pp. 121–154, 1987. https://doi.org/10.1257/jep.1.1.121
M. H. Birnbaum, “The Paradoxes of Allais, Stochastic Dominance, and Decision Weights,” in J. C. Shanteau, B. A, Mellers & D. A. Schum Eds. Decision Science and Technology. Reflections on the Contributions of Ward Edwards, Springer US, 1999. https://doi.org/10.1007/978-1-4615-5089-1_3
G. Wu and R. Gonzalez, “Common Consequence Condition in Decision Making under Risk,” Journal of Risk and Uncertainty, vol. 16, pp. 115– 139, 1998. https://doi.org/10.1023/A:1007714509322
H. Fehr-Duda and T. Epper, “Probability and Risk: Foundation and Economic Implications of Probability Dependent Risk Preferences,” The Annual Review of Economics, vol. 4, pp. 567–593, 2012. https://doi.org/10.1146/annurev-economics-080511-110950
P. J. H. Schoemaker, “The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations,” Journal of Economic Literature, vol. 20, no. 2, pp. 529–563, Jun. 1982.
E. U. Weber, “From Subjective Probabilities to Decision Weights: The Effect of Asymmetric Loss Function on the Evaluation of Uncertain Outcomes and Events,” Psychological Bulletin, vol. 15, no. 2, pp. 228– 242, March 1994. https://doi.org/10.1037/0033-2909.115.2.228
J. Quiggin, “A Theory of Anticipated Utility,” Journal of Economic Behavior and Organization, vol. 3, pp. 323–343, Dec. 1982. https://doi.org/10.1016/0167-2681(82)90008-7
D. Kahneman and A. Tversky, “A Prospect Theory,” Econometrica, vol. 47, no. 2, pp. 263–291, March 1979. https://doi.org/10.2307/1914185
P. Wakker, Prospect Theory for Risk and Ambiguity, Cambridge University Press, 2010. https://doi.org/10.1017/CBO9780511779329
D. Prelec, “The Probability Weighting Function”, Econometrica, vol. 66, no. 3, pp. 497–527, May 1998. https://doi.org/10.2307/2998573
Refbacks
- There are currently no refbacks.
Copyright (c) 2016 Oļegs Užga-Rebrovs, Gaļina Kuļešova
This work is licensed under a Creative Commons Attribution 4.0 International License.