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The Pearson system of utility functions

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Author Info

  • 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.

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File URL: http://128.118.178.162/eps/game/papers/0311/0311002.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 0311002.

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Length: 18 pages
Date of creation: 06 Nov 2003
Date of revision:
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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Web page: http://128.118.178.162

Related research

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.;

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References

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  1. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
  2. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
  3. Bell, David E & Fishburn, Peter C, 2000. " Utility Functions for Wealth," Journal of Risk and Uncertainty, Springer, vol. 20(1), pages 5-44, January.
  4. 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.
  5. Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-30, June.
  6. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
  7. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60, pages 151.
  8. Erio Castagnoli & Marco LiCalzi, 2005. "Expected utility without utility," Game Theory and Information 0508004, EconWPA.
  9. Wakker, Peter & Tversky, Amos, 1993. " An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-75, October.
  10. Neilson, William S, 2002. " Comparative Risk Sensitivity with Reference-Dependent Preferences," Journal of Risk and Uncertainty, Springer, vol. 24(2), pages 131-42, March.
  11. 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 247-57, August.
  12. Robert Bordley & Marco LiCalzi, 2000. "Decision analysis using targets instead of utility functions," Decisions in Economics and Finance, Springer, vol. 23(1), pages 53-74.
  13. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-54, January.
  14. 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.
  15. 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.
  16. Christian Gollier, 2004. "The Economics of Risk and Time," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262572249, December.
  17. 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.
  18. Marvin H. Berhold, 1973. "The Use of Distribution Functions to Represent Utility Functions," Management Science, INFORMS, vol. 19(7), pages 825-829, March.
  19. 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.
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Citations

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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. Meyer, Jack, 2007. "Representing Risk Preferences in Expected Utility Based Decision Models," SCC-76 Meeting, March 15-17, 2007, Gulf Shores, Alabama 9380, SCC-76: Economics and Management of Risk in Agriculture and Natural Resources.
  3. 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.

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