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Utility Functions for Wealth

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  • Bell, David E
  • Fishburn, Peter C

Abstract

We specify all utility functions on wealth implied by four special conditions on preferences between risky prospects in four theories of utility, under the presumption that preference increases in wealth. The theories are von Neumann-Morgenstern expected utility (EU), rank dependent utility (RDU), weighted linear utility (WLU), and skew-symmetric bilinear utility (SSBU). The special conditions are a weak version of risk neutrality, Pfanzagl's consistency axiom, Bell's one-switch condition, and a contextual uncertainty condition. Previous research has identified the functional forms for utility of wealth for all four conditions under EU, and for risk neutrality and Pfanzagl's consistency axiom under WLU and SSBU. The functional forms for the other condition-theory combinations are derived in this paper. Copyright 2000 by Kluwer Academic Publishers

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  • Bell, David E & Fishburn, Peter C, 2000. "Utility Functions for Wealth," Journal of Risk and Uncertainty, Springer, vol. 20(1), pages 5-44, January.
    • Handle: RePEc:kap:jrisku:v:20:y:2000:i:1:p:5-44
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    Cited by:

    1. Amedeo Piolatto & Matthew D. Rablen, 2017. "Prospect theory and tax evasion: a reconsideration of the Yitzhaki puzzle," Theory and Decision, Springer, vol. 82(4), pages 543-565, April.
    2. Cohen Alma, 2006. "The Disadvantages of Aggregate Deductibles," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 6(1), pages 1-28, April.
    3. LiCalzi, Marco & Sorato, Annamaria, 2006. "The Pearson system of utility functions," European Journal of Operational Research, Elsevier, vol. 172(2), pages 560-573, July.
    4. Nina Anchugina, 2017. "One-Switch Discount Functions," Papers 1702.02254, arXiv.org.
    5. Charles-Cadogan, G., 2016. "Expected utility theory and inner and outer measures of loss aversion," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 10-20.
    6. David E. Bell & Peter C. Fishburn, 2001. "Strong One-Switch Utility," Management Science, INFORMS, vol. 47(4), pages 601-604, April.
    7. Mikhail Sokolov, 2011. "Interval scalability of rank-dependent utility," Theory and Decision, Springer, vol. 70(3), pages 255-282, March.
    8. 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.
    9. Gollier, Christian & Schlesinger, Harris, 2003. "Preserving preference rankings under background risk," Economics Letters, Elsevier, vol. 80(3), pages 337-341, September.
    10. Henry Stott, 2006. "Cumulative prospect theory's functional menagerie," Journal of Risk and Uncertainty, Springer, vol. 32(2), pages 101-130, March.
    11. Liang Zou, 2006. "An Alternative to Prospect Theory," Annals of Economics and Finance, Society for AEF, vol. 7(1), pages 1-28, May.

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