In this paper we introduce a generalization of the De Vylder approximation. Our idea is to approximate the ruin probability with the one for a different process with gamma claims, matching first four moments. We compare the two approximations studying mixture of exponentials and lognormal...

The ruin probability in finite time can only be calculated analytically for a few special cases of the claim amount distribution. The most classic example is discussed in Section 1.2. The value can always be computed directly using Monte Carlo simulations, however, this is usually a...

We introduce here a diffusion-type approximation of the ruin probability both in finite and infinite time for a two-dimensional risk process, where claims and premiums are shared with a predetermined proportion. This type of process is often called the insurer-reinsurer model. We assume that the...