# On the asymptotic distribution of certain bivariate reinsurance treaties

### Details

Serval ID

serval:BIB_2A3D896729A5

Type

**Article**: article from journal or magazin.

Collection

Publications

Fund

Title

On the asymptotic distribution of certain bivariate reinsurance treaties

Journal

Insurance: Mathematics and Economics

ISSN

0167-6687

Publication state

Published

Issued date

2007

Peer-reviewed

Oui

Volume

40

Number

2

Pages

200-208

Language

english

Abstract

Let {(X-n, Y-n), n >= 1} be bivariate random claim sizes with common distribution function F and let {N(t), t >= 0} be a stochastic process which counts the number of claims that occur in the time interval [0, t], t >= 0. In this paper we derive the joint asymptotic distribution of randomly indexed order statistics of the random sample (X-1, Y-1), (X-2, Y-2), ... , (X-N ((t)), Y-N (t)) which is then used to obtain asymptotic representations for the joint distribution of two generalised largest claims reinsurance treaties available under specific insurance settings. As a by-product we obtain a stochastic representation of a m-dimensional Lambda-extremal variate in terms of iid unit exponential random variables.

Keywords

Generalised largest claims reinsurance treaty, Bivariate random order statistics, Bivariate treaties, Asymptotic results, Extreme value theory, m-Dimensional Lambda-Extremal variate

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Create date

03/09/2010 11:34

Last modification date

03/03/2018 15:22