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The Role of Some Functional Equations in Decision Analysis

Author

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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 61801)

  • János Aczél

    (Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada)

Abstract

This paper presents some functional equations that have played an essential role in the characterization of utility and probability functions in decision analysis. We survey some previous results with improvements and derive several new results. We also discuss some simple methods for the solution of these equations and highlight some subtle points about their use. We show that one functional equation can determine several unknown functions within it, and that relaxing differentiability and requiring only continuity of the functions leads to generalizations of many well-known results in utility and Bayesian probability theory.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ordeca:v:7:y:2010:i:2:p:215-228
    DOI: 10.1287/deca.1100.0177
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    References listed on IDEAS

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    1. James S. Dyer & Rakesh K. Sarin, 1982. "Relative Risk Aversion," Management Science, INFORMS, vol. 28(8), pages 875-886, August.
    2. Ali E. Abbas, 2007. "Invariant Utility Functions and Certain Equivalent Transformations," Decision Analysis, INFORMS, vol. 4(1), pages 17-31, March.
    3. David E. Bell, 1988. "One-Switch Utility Functions and a Measure of Risk," Management Science, INFORMS, vol. 34(12), pages 1416-1424, December.
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    Cited by:

    1. Ali E. Abbas, 2012. "Valuing Changes in Investment Opportunities," Operations Research, INFORMS, vol. 60(6), pages 1451-1460, December.
    2. Ali E. Abbas & David E. Bell, 2012. "METHODS---One-Switch Conditions for Multiattribute Utility Functions," Operations Research, INFORMS, vol. 60(5), pages 1199-1212, October.
    3. L. Robin Keller, 2011. "From the Editor ---Multiattribute and Intertemporal Preferences, Probability, and Stochastic Processes: Models and Assessment," Decision Analysis, INFORMS, vol. 8(3), pages 165-169, September.
    4. L. Robin Keller & Kelly M. Kophazi, 2011. "From the Editors---Deterrence, Multiattribute Utility, and Probability and Bayes' Updating," Decision Analysis, INFORMS, vol. 8(2), pages 83-87, June.
    5. L. Robin Keller & Kelly M. Kophazi, 2010. "From the Editors..," Decision Analysis, INFORMS, vol. 7(2), pages 151-154, June.

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