On some new dependence models derived from multivariate collective models in insurance applications

Consider two different portfolios which have claims triggered by the same events. Their corresponding collective model over a fixed time period is given in terms of individual claim sizes (Xi,Yi),i≥1$ (X_i,Y_i), i \ge 1 $ and a claim counting random variable N. In this paper, we are concerned with the joint distribution function (df) F of the largest claim sizes (XN:N,YN:N)$ (X_{N:N}, Y_{N:N}) $. By allowing N to depend on some parameter, say θ$ \theta $, then F=F(θ)$ F=F(\theta ) $ is for various choices of N a tractable parametric family of bivariate dfs. We investigate both distributional and extremal properties of (XN:N,YN:N)$ (X_{N:N}, Y_{N:N}) $. Furthermore, we present several applications of the implied parametric models to some data from the literature and a new data-set from a Swiss insurance company (Data-set can be downloaded here http://dx.doi.org/10.13140/RG.2.1.3082.9203.)