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On the use of Archimedean copulas for insurance modelling

Published online by Cambridge University Press:  17 June 2020

Thilini Dulanjali Kularatne ,
Jackie Li  and
David Pitt
Thilini Dulanjali Kularatne
Affiliation:
Department of Actuarial Studies and Business Analytics, Macquarie University, Sydney, New South Wales, Australia
Jackie Li*
Affiliation:
Department of Actuarial Studies and Business Analytics, Macquarie University, Sydney, New South Wales, Australia
David Pitt
Affiliation:
Department of Actuarial Studies and Business Analytics, Macquarie University, Sydney, New South Wales, Australia
*
*Corresponding author. E-mail: [email protected]
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Abstract

In this paper, we explore the use of an extensive list of Archimedean copulas in general and life insurance modelling. We consider not only the usual choices like the Clayton, Gumbel–Hougaard, and Frank copulas but also several others which have not drawn much attention in previous applications. First, we apply different copula functions to two general insurance data sets, co-modelling losses and allocated loss adjustment expenses, and also losses to building and contents. Second, we adopt these copulas for modelling the mortality trends of two neighbouring countries and calculate the market price of a mortality bond. Our results clearly show that the diversity of Archimedean copula structures gives much flexibility for modelling different kinds of data sets and that the copula and tail dependence assumption can have a significant impact on pricing and valuation. Moreover, we conduct a large simulation exercise to investigate further the caveats in copula selection. Finally, we examine a number of other estimation methods which have not been tested in previous insurance applications.

Keywords

Archimedean copulasTail dependenceLosses and allocated loss adjustment expensesMulti-population mortality modellingMortality bondEstimation methodsEmpirical copulas
Type
Paper
Information
Annals of Actuarial Science , Volume 15 , Issue 1 , March 2021 , pp. 57 - 81
Copyright
© Institute and Faculty of Actuaries 2020

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