On the asymptotic distribution of certain bivariate reinsurance treaties

Details On the asymptotic distribution of certain bivariate reinsurance treaties On the asymptotic distribution of certain bivariate reinsurance treaties

2006-03-30

arxiv.org/abs/math/0603719v2

Mathematics

Probability

11 pages

Scientific paper

Let (X_n,Y_n), n\ge 1 be bivariate random claim sizes with common distribution function F and let N(t), t \ge 0 be a stochastic process which counts the number of claims that occur in the time interval [0,t], t\ge 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.

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