Total loss estimation using copula-based regression models

Nicole Krämer, Eike C. Brechmann, Daniel Silvestrini and Claudia Czado

Insurance: Mathematics and Economics, 2013, vol. 53, issue 3, 829-839

Abstract: We present a joint copula-based model for insurance claims and sizes. It uses bivariate copulae to accommodate for the dependence between these quantities. We derive the general distribution of the policy loss without the restrictive assumption of independence. We illustrate that this distribution tends to be skewed and multi-modal, and that an independence assumption can lead to substantial bias in the estimation of the policy loss. Further, we extend our framework to regression models by combining marginal generalized linear models with a copula. We show that this approach leads to a flexible class of models, and that the parameters can be estimated efficiently using maximum-likelihood. We propose a test procedure for the selection of the optimal copula family. The usefulness of our approach is illustrated in a simulation study and in an analysis of car insurance policies.

Keywords: Dependence modeling; Generalized linear model; Number of claims; Claim size; Policy loss (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (26)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:53:y:2013:i:3:p:829-839

DOI: 10.1016/j.insmatheco.2013.09.003

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