Transform approach for discounted aggregate claims in a risk model with descendant claims

We consider a risk model with three types of claims: ordinary, leading, and descendant claims. We derive an expression for the Laplace–Stieltjes transform of the distribution of the discounted aggregate claims. By using this expression, we can then obtain the mean and variance of the discounted aggregate claims. For actuarial applications, the VaR and CTE are computed by numerical inversion of the Laplace transforms for the tail probability and the conditional tail expectation of the discounted aggregate claims. The net premium for stop-loss reinsurance contract is also computed.