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Consider two different portfolios which have claims triggered by the sameevents. Their corresponding collective model over a fixed time period is givenin terms of individual claim sizes $(X_i,Y_i), i\ge 1$ and a claim countingrandom variable $N$. In this paper we are concerned with the joint distributionfunction $F$ of the \ece{largest claim sizes} $(X_{N:N}, Y_{N:N})$. By allowing$N$ to depend on some parameter, say $\theta$, then $F=F(\theta)$ is forvarious choices of $N$ a tractable parametric family of bivariate distributionfunctions. We present three applications of the implied parametric models tosome data from the literature and a new data set from a Swiss insurancecompany. Furthermore, we investigate both distributional and asymptoticproperties of $(X_{N:N}, Y_{N:N})$.

Insurance Applications of Some New Dependence Models derived from Multivariate Collective Models