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One-Switch Utility Functions and a Measure of Risk

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  • David E. Bell

    (Harvard Business School, Soldiers Field, Boston, Massachusetts 02163)

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    Abstract

    Consider the relative attractiveness to a decision maker of two financial gambles as the wealth of that individual varies. It may seem reasonable that either one alternative should be preferred for all wealth levels or that there exists a unique critical wealth level at which the decision maker switches from preferring one alternative to the other. Decreasing risk aversion is not sufficient for this property to hold: we identify the small class of utility functions for which it does. We show how the property leads naturally to a measure of risk. The results of this paper apply equally well to discounting functions for cash flows: one-switch discount functions permit at most one change in preference between cash flows as all payoffs are deferred in time.

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    File URL: http://dx.doi.org/10.1287/mnsc.34.12.1416
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 34 (1988)
    Issue (Month): 12 (December)
    Pages: 1416-1424

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    Handle: RePEc:inm:ormnsc:v:34:y:1988:i:12:p:1416-1424

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    Related research

    Keywords: decision analysis; utility theory; risk; discounting;

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    Cited by:
    1. Liu, Liqun & Meyer, Jack, 2013. "Substituting one risk increase for another: A method for measuring risk aversion," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2706-2718.
    2. Denis Conniffe, 2007. "Generalised Means of Simple Utility Functions with Risk Aversion," Economics, Finance and Accounting Department Working Paper Series n1790907.pdf, Department of Economics, Finance and Accounting, National University of Ireland - Maynooth.
    3. Dionne, Georges & Li, Jingyuan, 2014. "Comparative Ross risk aversion in the presence of mean dependent risks," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 128-135.
    4. Gollier, Christian, 2002. "Time Horizon and the Discount Rate," Journal of Economic Theory, Elsevier, vol. 107(2), pages 463-473, December.
    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. Denuit, Michel M. & Eeckhoudt, Louis & Schlesinger, Harris, 2013. "When Ross meets Bell: The linex utility function," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 177-182.
    7. Mitchell, Douglas W. & Gelles, Gregory M., 2003. "Risk-value models: Restrictions and applications," European Journal of Operational Research, Elsevier, vol. 145(1), pages 109-120, February.
    8. Eugenio Peluso & Alain Trannoy, 2012. "The Cake-eating problem: Non-linear sharing rules," Working Papers 26/2012, University of Verona, Department of Economics.
    9. Sancetta, A., 2005. "Copula Based Monte Carlo Integration in Financial Problems," Cambridge Working Papers in Economics 0506, Faculty of Economics, University of Cambridge.
    10. Kang, Byung Jin & Kim, Tong Suk, 2006. "Option-implied risk preferences: An extension to wider classes of utility functions," Journal of Financial Markets, Elsevier, vol. 9(2), pages 180-198, May.
    11. Nakamura, Yutaka, 1996. "Sumex utility functions," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 39-47, February.
    12. Gollier, Christian, 2002. "Discounting an uncertain future," Journal of Public Economics, Elsevier, vol. 85(2), pages 149-166, August.
    13. Georges Dionne & Jingyuan Li, 2012. "Comparative Ross Risk Aversion in the Presence of Quadrant Dependent Risks," Cahiers de recherche 1226, CIRPEE.
    14. Ali E. Abbas & James E. Matheson & Robert F. Bordley, 2009. "Effective utility functions induced by organizational target-based incentives," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 30(4), pages 235-251.
    15. Gelles, Gregory M. & Mitchell, Douglas W., 2002. "Increasingly mean-seeking utility functions and n-asset portfolios," The Quarterly Review of Economics and Finance, Elsevier, vol. 42(5), pages 911-919.
    16. BakIr, Niyazi Onur & Klutke, Georgia-Ann, 2011. "Information and preference reversals in lotteries," European Journal of Operational Research, Elsevier, vol. 210(3), pages 752-756, May.
    17. Jim Musumeci & Joe Musumeci, 1999. "A Dynamic-Programming Approach to Multiperiod Asset Allocation," Journal of Financial Services Research, Springer, vol. 15(1), pages 5-21, February.
    18. Gollier, Christian & Schlesinger, Harris, 2003. "Preserving preference rankings under background risk," Economics Letters, Elsevier, vol. 80(3), pages 337-341, September.

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