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Archimedean copulas derived from Morgenstern utility functions

Spreeuw, J. (2012). Archimedean copulas derived from Morgenstern utility functions (Actuarial Research Paper No. 201). London, UK: Faculty of Actuarial Science & Insurance, City University London.


The (additive) generator of an Archimedean copula - as well as the inverse of the generator - is a strictly decreasing and convex function, while Morgenstern utility functions (applying to risk averse decision makers) are nondecreasing and concave. This provides a basis for deriving either a generator of Archimedean copulas, or its inverse, from a Morgenstern utility function. If we derive the generator in this way, dependence properties of an Archimedean copula that are often taken to be desirable, match with generally sought after properties of the corresponding utility function. It is shown how well known copula families are derived from established utility functions. Also, some new copula families are derived, and their properties are discussed. If, on the other hand, we instead 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.

Publication Type: Monograph (Working Paper)
Publisher Keywords: copula, Archimedean generator, utility function, risk aversion, dependence
Subjects: H Social Sciences > HG Finance
Departments: Bayes Business School > Actuarial Science & Insurance > Actuarial Research Reports
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