ON THE IMPACT OF HIDDEN TRENDS FOR A COMPOUND POISSON MODEL WITH PARETO-TYPE CLAIMS

We consider a compound-Poisson model with Pareto-type claims. In contrast to the classical case, where the claims are assumed to be iid., we assume that scaling and location parameters of the Pareto distribution follow a certain trend. We investigate the impact of this trend on parameter estimation and on the VaR (Value-at-Risk), if one mis-specifies (or even neglects) this trend. In the first part we show a consistency result for the mis-specified model, in the second part the deviations of the true parameters from the ones obtained by applying an iid. procedure is measured. Finally we study the impact of the mis-specification on a typical risk measure like the VaR.