Fitting and validation of a bivariate model for large claims

We consider an extended version of a model proposed by Ledford and Tawn [Ledford, A.W., Tawn, J.A., 1997. Modelling dependence within joint tail regions. J. R. Stat. Soc. 59 (2), 475–499] for the joint tail distribution of a bivariate random vector, which essentially assumes an asymptotic power scaling law for the probability that both the components of the vector are jointly large. After discussing how to fit the model, we devise a graphical tool that analyzes the differences between certain empirical probabilities and model based estimates of the same probabilities. The asymptotic normality of these differences allows the construction of statistical tests for the model assumption. The results are applied to claims of a Danish fire insurance and to medical claims from US health insurances.