  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.
