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Constant Exchange Risk Properties

Author

Listed:
  • Peter H. Farquhar

    (Carnegie-Mellon University, Pittsburgh, Pennsylvania)

  • Yutaka Nakamura

    (Osaka University, Osaka, Japan)

Abstract

This paper develops a methodology using risk properties to characterize the functional form of a utility measure for decision making under uncertainty. The constant absolute risk property, for example, is known to be necessary and sufficient, with appropriate regularity conditions, for the utility function to have either a linear or an exponential form. A new generalization of this property, called the constant exchange risk property, gives a characterization of six utility functions: the linear function, the exponential function, the quadratic function, the sum of two exponential functions, the sum of a linear and an exponential function, and the product of a linear and an exponential function. Since all of these functional forms have been used previously as approximations, this methodology allows analysts to distinguish beforehand between alternative forms and thus properly specify the utility function in applications.

Suggested Citation

  • Peter H. Farquhar & Yutaka Nakamura, 1987. "Constant Exchange Risk Properties," Operations Research, INFORMS, vol. 35(2), pages 206-214, April.
    • Handle: RePEc:inm:oropre:v:35:y:1987:i:2:p:206-214
    DOI: 10.1287/opre.35.2.206
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    Citations

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    Cited by:

    1. David E. Bell & Peter C. Fishburn, 2001. "Strong One-Switch Utility," Management Science, INFORMS, vol. 47(4), pages 601-604, April.
    2. Horst Zank, 2001. "Cumulative Prospect Theory for Parametric and Multiattribute Utilities," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 67-81, February.
    3. Thomas Eichner, 2008. "Mean Variance Vulnerability," Management Science, INFORMS, vol. 54(3), pages 586-593, March.
    4. Nakamura, Yutaka, 2015. "Mean-variance utility," Journal of Economic Theory, Elsevier, vol. 160(C), pages 536-556.
    5. Zank H., 1998. "Cumulative Prospect Theory for Parametric and Multiattribute Utilities," Research Memorandum 008, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    6. Conniffe, Denis, 2008. "Generalised Means of Simple Utility Functions with Risk Aversion," The Economic and Social Review, Economic and Social Studies, vol. 39(1), pages 1-12.
    7. LiCalzi, Marco & Sorato, Annamaria, 2006. "The Pearson system of utility functions," European Journal of Operational Research, Elsevier, vol. 172(2), pages 560-573, July.
    8. Zank, H., 1998. "Cumulative prospect theory for parametric and multiattribute utilities," Research Memorandum 019, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    9. Craig W. Kirkwood, 2004. "Approximating Risk Aversion in Decision Analysis Applications," Decision Analysis, INFORMS, vol. 1(1), pages 51-67, March.
    10. Nakamura, Yutaka, 1996. "Sumex utility functions," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 39-47, February.

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