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Relationships Between Archimedean Copulas and Morgenstern Utility Functions

Spreeuw, J. (2010). Relationships Between Archimedean Copulas and Morgenstern Utility Functions. In: Lecture Notes in Statistics: Proceedings of the Workshop Held in Warsaw, 25-26 September 2009. Copula Theory and Its Applications, 25-26 September 2009, Warsaw.


The (additive) generator of an Archimedean copula is a strictly decreasing and convexfunction, while Morgenstern utility functions (applying to risk aversion decision makers) arenondecreasing and concave. In this presentation, relationships between generators and utilityfunctions are established. For some well known Archimedean copula families, links betweenthe generator and the corresponding utility function are demonstrated.Some new copulafamilies are derived from classes of utility functions which appeared in the literature, andtheir properties are discussed. It is shown how dependence properties of an Archimedeancopula translate into properties of the utility function from whichthey are constructed.

Publication Type: Conference or Workshop Item (Lecture)
Additional Information: The final publication is available at Springer via
Publisher Keywords: Copulas - Dependence concepts - Reliability theory - Risk aggregation - Stochastic models
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Departments: Bayes Business School > Actuarial Science & Insurance
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