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The Pearson system of utility functions

Author

Listed:
  • Marco LiCalzi

    (University of Venice)

  • Annamaria Sorato

    (University of Venice)

Abstract

This paper describes a parametric family of utility functions for decision analysis. The parameterization is obtained by embedding the HARA class in a four-parameter representation for the risk aversion function. The resulting utility functions have only four shapes: concave, convex, S-shaped, and reverse S-shaped. This makes the family suited for both expected utility and prospect theory. We also describe an alternative technique to estimate the four parameters from elicited utilities, which is simpler and easier to implement than standard fitting by minimization of the mean quadratic error.

Suggested Citation

  • Marco LiCalzi & Annamaria Sorato, 2003. "The Pearson system of utility functions," Game Theory and Information 0311002, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:0311002
    Note: Type of Document - pdf; prepared on Mac OsX; to print on A4 paper; pages: 18
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    Cited by:

    1. Denis Conniffe, 2007. "The Generalised Extreme Value Distribution as Utility Function," The Economic and Social Review, Economic and Social Studies, vol. 38(3), pages 275-288.
    2. Fausto Corradin & Domenico Sartore, 2020. "Risk Aversion: Differential Conditions for the Iso-Utility Curves with Positive Slope in Transformed Two-Parameter Distributions," Advances in Decision Sciences, Asia University, Taiwan, vol. 24(3), pages 142-217, September.
    3. Chang, Ching-Ter, 2011. "Multi-choice goal programming with utility functions," European Journal of Operational Research, Elsevier, vol. 215(2), pages 439-445, December.
    4. Jack Meyer, 2010. "Representing risk preferences in expected utility based decision models," Annals of Operations Research, Springer, vol. 176(1), pages 179-190, April.
    5. Abbas, Ali E., 2007. "Moments of utility functions and their applications," European Journal of Operational Research, Elsevier, vol. 180(1), pages 378-395, July.
    6. Brett Houlding & Frank P. A. Coolen & Donnacha Bolger, 2015. "A Conjugate Class of Utility Functions for Sequential Decision Problems," Risk Analysis, John Wiley & Sons, vol. 35(9), pages 1611-1622, September.
    7. Joost M.E. Pennings & Philip Garcia, 2009. "The informational content of the shape of utility functions: financial strategic behavior," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 30(2), pages 83-90.
    8. Fausto Corradin & Domenico Sartore, 2020. "Risk Aversion: Differential Conditions for the Iso-Utility Curves with Positive Slope in Transformed Two-Parameter Distributions," Advances in Decision Sciences, Asia University, Taiwan, vol. 24(3), pages 142-217, September.
    9. Taras Bodnar & Dmytro Ivasiuk & Nestor Parolya & Wolfgang Schmid, 2023. "Multi-period power utility optimization under stock return predictability," Computational Management Science, Springer, vol. 20(1), pages 1-27, December.
    10. Zhengwei Sun & Ali E. Abbas, 2014. "On the sensitivity of the value of information to risk aversion in two-action decision problems," Environment Systems and Decisions, Springer, vol. 34(1), pages 24-37, March.

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    More about this item

    Keywords

    coefficient of risk aversion; elicitation of preferences under risk; expected utility; HARA utility functions; Pearson system of distributions; prospect theory; probability weighting function; target- based decisions.;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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