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One-Switch Utility Functions and a Measure of Risk


  • David E. Bell

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


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.

Suggested Citation

  • David E. Bell, 1988. "One-Switch Utility Functions and a Measure of Risk," Management Science, INFORMS, vol. 34(12), pages 1416-1424, December.
  • Handle: RePEc:inm:ormnsc:v:34:y:1988:i:12:p:1416-1424

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    References listed on IDEAS

    1. Leech, Dennis, 1985. "Ownership Concentration and the Theory of the Firm : A Simple-Game-Theoretic Approach to Applied US Corporations in the 1930's," The Warwick Economics Research Paper Series (TWERPS) 262, University of Warwick, Department of Economics.
    2. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
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    decision analysis; utility theory; risk; discounting;


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