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Utility Copula Functions Matching All Boundary Assessments

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)

Abstract

The construction of a multiattribute utility function is an important step in decision analysis and can be a challenging task unless some decomposition of the utility function is performed. When every attribute is utility independent of its complement, the utility elicitation task is significantly simplified because the functional form of the utility function requires only one conditional utility function for each attribute, and some normalizing constants. When utility independence conditions do not hold, the conditional utility function of an attribute may vary across the domain of the complement attributes, and therefore a single conditional utility assessment for each attribute may not be sufficient to capture the decision maker's preferences. This paper proposes a method to construct utility functions that have the flexibility to match the variations in the conditional utility function, across the domain of the attributes, using univariate utility assessments at the boundary values. The approach incorporates the boundary assessments into a new function, which we call the double-sided utility copula. This formulation provides a wealth of new functional forms that the analyst may use to incorporate utility dependence in multiattribute decision problems. The utility copula function also allows for the flexibility to incorporate a wide range of trade-off assessments among the attributes, while keeping the utility assessments at the boundary values fixed. It is also useful in determining the order of approximation provided by using certain independence assumptions in a multiattribute decision problem when the attributes are utility dependent.

Suggested Citation

  • Ali E. Abbas, 2013. "Utility Copula Functions Matching All Boundary Assessments," Operations Research, INFORMS, vol. 61(2), pages 359-371, April.
  • Handle: RePEc:inm:oropre:v:61:y:2013:i:2:p:359-371
    DOI: 10.1287/opre.1120.1152
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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 & David E. Bell, 2011. "One-Switch Independence for Multiattribute Utility Functions," Operations Research, INFORMS, vol. 59(3), pages 764-771, June.
    3. Ali E. Abbas, 2009. "Multiattribute Utility Copulas," Operations Research, INFORMS, vol. 57(6), pages 1367-1383, December.
    4. Craig W. Kirkwood, 1976. "Parametrically Dependent Preferences for Multiattributed Consequences," Operations Research, INFORMS, vol. 24(1), pages 92-103, February.
    5. Ali E. Abbas, 2011. "The Multiattribute Utility Tree," Decision Analysis, INFORMS, vol. 8(3), pages 180-205, September.
    6. Ali E. Abbas & Ronald A. Howard, 2005. "Attribute Dominance Utility," Decision Analysis, INFORMS, vol. 2(4), pages 185-206, December.
    7. Peter H. Farquhar, 1975. "A Fractional Hypercube Decomposition Theorem for Multiattribute Utility Functions," Operations Research, INFORMS, vol. 23(5), pages 941-967, October.
    8. David E. Bell, 1979. "Multiattribute Utility Functions: Decompositions Using Interpolation," Management Science, INFORMS, vol. 25(8), pages 744-753, August.
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    Cited by:

    1. Plischke, Elmar & Borgonovo, Emanuele, 2019. "Copula theory and probabilistic sensitivity analysis: Is there a connection?," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1046-1059.
    2. Ali E. Abbas & Zhengwei Sun, 2019. "Archimedean Utility Copulas with Polynomial Generating Functions," Decision Analysis, INFORMS, vol. 16(3), pages 218-237, September.
    3. Ying He & James S. Dyer & John C. Butler, 2014. "Decomposing a Utility Function Based on Discrete Distribution Independence," Decision Analysis, INFORMS, vol. 11(4), pages 233-249, December.
    4. Zifeng Zhao & Peng Shi & Xiaoping Feng, 2021. "Knowledge Learning of Insurance Risks Using Dependence Models," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1177-1196, July.
    5. Ali E. Abbas & Zhengwei Sun, 2015. "Multiattribute Utility Functions Satisfying Mutual Preferential Independence," Operations Research, INFORMS, vol. 63(2), pages 378-393, April.

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