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.