The Pearson system of utility functions
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.
|Date of creation:||06 Nov 2003|
|Note:||Type of Document - pdf; prepared on Mac OsX; to print on A4 paper; pages: 18|
|Contact details of provider:|| Web page: http://econwpa.repec.org|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Marvin H. Berhold, 1973. "The Use of Distribution Functions to Represent Utility Functions," Management Science, INFORMS, vol. 19(7), pages 825-829, March.
- Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60, pages 151-151.
- 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.
- Neilson, William S, 2002. "Comparative Risk Sensitivity with Reference-Dependent Preferences," Journal of Risk and Uncertainty, Springer, vol. 24(2), pages 131-142, March.
- Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-154, January.
- Christian Gollier, 2004. "The Economics of Risk and Time," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262572249, July.
- Erio Castagnoli & Marco LiCalzi, 2005. "Expected utility without utility," Game Theory and Information 0508004, EconWPA.
- David E. Bell, 1988. "One-Switch Utility Functions and a Measure of Risk," Management Science, INFORMS, vol. 34(12), pages 1416-1424, December.
- Karl Borch, 1968. "Decision Rules Depending On The Probability Of Ruin," Oxford Economic Papers, Oxford University Press, vol. 20(1), pages 1-10.
- Kimball, Miles S, 1993.
"Standard Risk Aversion,"
Econometric Society, vol. 61(3), pages 589-611, May.
- Miles S. Kimball, 1991. "Standard Risk Aversion," NBER Technical Working Papers 0099, National Bureau of Economic Research, Inc.
- 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.
- Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
- Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
- 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.
- Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
- 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.
- Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-430, June.
- Peter H. Farquhar, 1984. "State of the Art---Utility Assessment Methods," Management Science, INFORMS, vol. 30(11), pages 1283-1300, November.
- Bell, David E & Fishburn, Peter C, 2000. "Utility Functions for Wealth," Journal of Risk and Uncertainty, Springer, vol. 20(1), pages 5-44, January.
- 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.
- Wakker, Peter & Tversky, Amos, 1993. "An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-175, October.
- Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November. Full references (including those not matched with items on IDEAS)