Risk Analysis of the Copula Dependent Aggregate Discounted Claims with Weibull Inter-Arrival Time

We model the recursive moments of aggregate discounted claims, assuming inter-claim arrival time follows a Weibull distribution to accommodate overdispersed and underdispersed data set. use copula represent dependence structure between its subsequent claim amount. then Laplace inversion via Gaver-Stehfest algorithm solve numerically first second moments, which takes form Volterra integral equation (VIE). compute average variance claims under Farlie-Gumbel-Morgenstern (FGM) conduct sensitivity analysis various parameters claim-size parameters. The comparison equidispersed, counting processes shows that when arrive at times vary more than is expected, insured lives can expect pay higher premium, vice versa for case arriving less expected. Upon comparing risk process with an equivalent Poisson process, we also found copulas wider range dependency parameter such as Frank Heavy Right Tail (HRT), have greater impact on value opposed modeling FGM weak structure.