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Archimedean copulas derived from utility functions

Spreeuw, J. (2014). Archimedean copulas derived from utility functions. Insurance: Mathematics and Economics, 59, pp. 235-242. doi: 10.1016/j.insmatheco.2014.10.002

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 modelling dependence of coupled lives is included.

Publication Type: Article
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Insurance: Mathematics and Economics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Insurance: Mathematics and Economics Volume 59, November 2014, Pages 235–242, http://dx.doi.org/10.1016/j.insmatheco.2014.10.002.
Publisher Keywords: copula, Archimedean generator, utility function, risk aversion, dependence
Subjects: H Social Sciences > HG Finance
Departments: Cass Business School > Actuarial Science & Insurance
URI: http://openaccess.city.ac.uk/id/eprint/5030
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