In this paper we consider a jump-diffusion type approximation of the classical risk process by a gamma Levy process. We derive here the asymptotic behavior (lower and upper bounds) of the finite time ruin probability for any gamma Levy process.

This chapter develops on risk processes which, perhaps, are most suitable for computer visualization of all insurance objects. At the same time, risk processes are basic instruments for any non-life actuary – they are vital for calculating the amount of loss that an insurance company may incur.

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...