Ruin probability for generalized φ-sub-Gaussian fractional Brownian motion

Abstract

In this paper we investigate the ruin problem for the generalized φ-sub-Gaussian fractional Brownian motion (FBM). Such random process has the same covariation function as FBM but its trajectories belong to the space of φ-sub-Gaussian random variables (i.e. not necessarily Gaussian). For this risk process we obtain estimate of the ruin probability.