Laplace transform on the recursive moments of aggregate discounted claims with Weibull interwaiting time

We consider aggregate discounted claims of a risk portfolio with Weibull counting process and compute its recursive moments numerically via the Laplace transform. We define the dependence structure between the inter-claim arrival time and its subsequent claims size using the Farlie-Gumbel-Morgenstern (FGM) copula. In our numerical examples, we compare the moments and conduct sensitivity analysis assuming an exponential and a Pareto claims size distribution. We found that despite having similar marginal variances, the risk portfolio with Pareto claims size produces larger moments compared to the corresponding exponential claims size.