IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpga/0311002.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0311/0311002.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Karl Borch, 1968. "Decision Rules Depending On The Probability Of Ruin," Oxford Economic Papers, Oxford University Press, vol. 20(1), pages 1-10.
    2. Peter H. Farquhar & Yutaka Nakamura, 1987. "Constant Exchange Risk Properties," Operations Research, INFORMS, vol. 35(2), pages 206-214, April.
    3. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    4. Neilson, William S & Stowe, Jill, 2002. "A Further Examination of Cumulative Prospect Theory Parameterizations," Journal of Risk and Uncertainty, Springer, vol. 24(1), pages 31-46, January.
    5. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    6. Robert Bordley & Marco LiCalzi, 2000. "Decision analysis using targets instead of utility functions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 23(1), pages 53-74.
    7. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    8. 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.
    9. Han Bleichrodt & Jose Luis Pinto, 2000. "A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis," Management Science, INFORMS, vol. 46(11), pages 1485-1496, November.
    10. Marvin H. Berhold, 1973. "The Use of Distribution Functions to Represent Utility Functions," Management Science, INFORMS, vol. 19(7), pages 825-829, March.
    11. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60, pages 151-151.
    12. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    13. Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-430, June.
    14. Peter Wakker & Daniel Deneffe, 1996. "Eliciting von Neumann-Morgenstern Utilities When Probabilities Are Distorted or Unknown," Management Science, INFORMS, vol. 42(8), pages 1131-1150, August.
    15. Neilson, William S, 2002. "Comparative Risk Sensitivity with Reference-Dependent Preferences," Journal of Risk and Uncertainty, Springer, vol. 24(2), pages 131-142, March.
    16. Peter H. Farquhar, 1984. "State of the Art---Utility Assessment Methods," Management Science, INFORMS, vol. 30(11), pages 1283-1300, November.
    17. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-154, January.
    18. Bell, David E & Fishburn, Peter C, 2000. "Utility Functions for Wealth," Journal of Risk and Uncertainty, Springer, vol. 20(1), pages 5-44, January.
    19. Christian Gollier, 2004. "The Economics of Risk and Time," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262572249, March.
    20. Cass, David & Stiglitz, Joseph E., 1970. "The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds," Journal of Economic Theory, Elsevier, vol. 2(2), pages 122-160, June.
    21. Wakker, Peter & Tversky, Amos, 1993. "An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-175, October.
    22. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
    23. Erio Castagnoli & Marco LiCalzi, 2005. "Expected utility without utility," Game Theory and Information 0508004, University Library of Munich, Germany.
    24. David E. Bell, 1988. "One-Switch Utility Functions and a Measure of Risk," Management Science, INFORMS, vol. 34(12), pages 1416-1424, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chang, Ching-Ter, 2011. "Multi-choice goal programming with utility functions," European Journal of Operational Research, Elsevier, vol. 215(2), pages 439-445, December.
    2. Abbas, Ali E., 2007. "Moments of utility functions and their applications," European Journal of Operational Research, Elsevier, vol. 180(1), pages 378-395, July.
    3. Jack Meyer, 2010. "Representing risk preferences in expected utility based decision models," Annals of Operations Research, Springer, vol. 176(1), pages 179-190, April.
    4. 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.
    5. 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.

    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.;

    JEL classification:

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpga:0311002. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.