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Valuing Changes in Investment Opportunities

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  • Ali E. Abbas

    (Department of Industrial and Enterprise Systems Engineering, College of Engineering, University of Illinois at Urbana--Champaign, Urbana, Illinois 61820)

Abstract

Arrow and Pratt introduced a measure of risk aversion---the negative ratio of the second to the first derivative of the utility function. This measure has found widespread use in the valuation of uncertain lotteries and in the calculation of the risk premium of an investment. This paper introduces two new measures for characterizing changes in the valuation of uncertain lotteries when their outcomes are modified by a monotone transformation. The first is a characteristic transformation of a utility function, U , and a monotone transformation, g . The shape of the characteristic transformation determines an upper bound, lower bound, or equality on the magnitude of the certainty equivalent of the modified lottery. The second is a measure of change in certainty equivalent, (eta) g , whose sign also determines upper or lower bounds, and whose magnitude determines the change in value of a “small-risk” lottery when its outcomes are modified by a monotone transformation. For shift (and scale) transformations on the lottery outcomes, both the characteristic transformation and the measure of change, (eta) g , provide new characterizations for the notions of decreasing absolute (and relative) risk aversion with wealth.

Suggested Citation

  • Ali E. Abbas, 2012. "Valuing Changes in Investment Opportunities," Operations Research, INFORMS, vol. 60(6), pages 1451-1460, December.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:6:p:1451-1460
    DOI: 10.1287/opre.1120.1092
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    References listed on IDEAS

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    1. Scott F. Richard, 1975. "Multivariate Risk Aversion, Utility Independence and Separable Utility Functions," Management Science, INFORMS, vol. 22(1), pages 12-21, September.
    2. Ali E. Abbas & János Aczél, 2010. "The Role of Some Functional Equations in Decision Analysis," Decision Analysis, INFORMS, vol. 7(2), pages 215-228, June.
    3. Ross, Stephen A, 1981. "Some Stronger Measures of Risk Aversion in the Small and the Large with Applications," Econometrica, Econometric Society, vol. 49(3), pages 621-638, May.
    4. Ali E. Abbas, 2007. "Invariant Utility Functions and Certain Equivalent Transformations," Decision Analysis, INFORMS, vol. 4(1), pages 17-31, March.
    5. Dybvig, Philip H & Lippman, Steven A, 1983. "An Alternative Characterization of Decreasing Absolute Risk Aversion," Econometrica, Econometric Society, vol. 51(1), pages 223-224, January.
    6. Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, October.
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    Cited by:

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