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Archimedean copulas derived from utility functions

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  • Spreeuw, Jaap

Abstract

The inverse of the (additive) generator of an Archimedean copula is a strictly decreasing and convex function, while utility functions (applying to risk averse decision makers) are nondecreasing and concave. This provides a basis for deriving an inverse generator of an Archimedean copula from a utility function. If we derive the inverse of the generator from the utility function, there is a link between the magnitude of measures of risk attitude (like the very common Arrow–Pratt coefficient of absolute risk aversion) and the strength of dependence featured by the corresponding Archimedean copula. Some new copula families are derived, and their properties are discussed. A numerical example about modeling dependence of coupled lives is included.

Suggested Citation

  • Spreeuw, Jaap, 2014. "Archimedean copulas derived from utility functions," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 235-242.
    • Handle: RePEc:eee:insuma:v:59:y:2014:i:c:p:235-242
    DOI: 10.1016/j.insmatheco.2014.10.002
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    References listed on IDEAS

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    Cited by:

    1. Nappo Giovanna & Spizzichino Fabio, 2020. "Relations between ageing and dependence for exchangeable lifetimes with an extension for the IFRA/DFRA property," Dependence Modeling, De Gruyter, vol. 8(1), pages 1-33, January.
    2. Liu, Ruixuan & Yu, Zhengfei, 2022. "Sample selection models with monotone control functions," Journal of Econometrics, Elsevier, vol. 226(2), pages 321-342.
    3. Nappo Giovanna & Spizzichino Fabio, 2020. "Relations between ageing and dependence for exchangeable lifetimes with an extension for the IFRA/DFRA property," Dependence Modeling, De Gruyter, vol. 8(1), pages 1-33, January.
    4. Jaap Spreeuw, 2022. "The Copula Derived from the SAHARA Utility Function," Risks, MDPI, vol. 10(7), pages 1-10, June.

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    More about this item

    Keywords

    IM10; IE12; IE43; Copula; Archimedean generator; Utility function; Risk aversion; Dependence;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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