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Mixture copulas and insurance applications

Published online by Cambridge University Press:  26 April 2018

Maissa Tamraz
Maissa Tamraz*
Affiliation:
Department of Actuarial Science, University of Lausanne, UNIL-Dorigny, 1015 Lausanne, Switzerland
*
*Correspondence to: Maissa Tamraz, Université de Lausanne, Faculté des Hautes Etudes Commerciales, Quartier UNIL-Chamberonne, Bâtiment Extranef, 1015 Lausanne, Switzerland. Tél: 021 692 33 00. E-mail: [email protected]
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Abstract

In the classical collective model over a fixed time period of two insurance portfolios, we are interested, in this contribution, in the models that relate to the joint distribution F of the largest claim amounts observed in both insurance portfolios. Specifically, we consider the tractable model where the claim counting random variable N follows a discrete-stable distribution with parameters (α,λ). We investigate the dependence property of F with respect to both parameters α and λ. Furthermore, we present several applications of the new model to concrete insurance data sets and assess the fit of our new model with respect to other models already considered in some recent contributions. We can see that our model performs well with respect to most data sets.

Keywords

Discrete-stable distributionCopulaParameter estimationLargest claimsGoodness of fit
Type
Paper
Information
Annals of Actuarial Science , Volume 12 , Issue 2 , September 2018 , pp. 391 - 411
Copyright
© Institute and Faculty of Actuaries 2018 

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