# Insurance Applications of Some New Dependence Models Derived from Multivariate Collective Models

21 Pages Posted: 8 Mar 2016 Last revised: 23 Jun 2017

See all articles by Enkelejd Hashorva

## Enkelejd Hashorva

University of Lausanne, Actuarial Department

## Gildas Ratovomirija

University of Lausanne

## Maissa Tamraz

Universite de Lausanne; Nankai University

Date Written: March 4, 2016

### Abstract

Consider two different portfolios which have claims triggered by the same events. Their corresponding collective model over a fixed time period is given in terms of individual claim sizes $(X_i,Y_i), i\ge 1$ and a claim counting random variable $N$. In this paper we are concerned with the joint distribution function $F$ of the largest claim sizes $(X_{N:N}, Y_{N:N})$. By allowing $N$ to depend on some parameter, say $\theta$, then $F=F(\theta)$ is for various choices of $N$ a tractable parametric family of bivariate distribution functions. We present three applications of the implied parametric models to some data from the literature and a new data set from a Swiss insurance company. Furthermore, we investigate both distributional and asymptotic properties of $(X_{N:N,Y_{N:N})$.

Keywords: Largest claims; copula; loss and ALAE; max-stable distribution; estimation; parametric family.

JEL Classification: G22

Suggested Citation

Hashorva, Enkelejd and Ratovomirija, Gildas and Tamraz, Maissa, Insurance Applications of Some New Dependence Models Derived from Multivariate Collective Models (March 4, 2016). Available at SSRN: https://ssrn.com/abstract=2742175 or http://dx.doi.org/10.2139/ssrn.2742175

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