Computing the Ruin Probability of Lévy Insurance Risk Processes in non-Cramér Models

Abstract

This study provides the explicit computation of the ruin probability of a Le¢vy process on finite time horizon in Theorem 1 with the help of a fluctuation identity. This paper also gives the numerical results of the ruin probability in Variance Gamma(VG) and Normal Inverse Gaussian(NIG) models as illustrations. Besides, the paths of VG and NIG processes are simulated using the same parameter values as in Madan et al. (1998).