PH approximation of two-barrier ruin probability for Lévy risk having two-sided PH jumps

Abstract

In this paper, we study a Lévy risk process consisting of Brownian component together with premiums and claims that are phase-type with many phases. Our aim is to approximate the probability of ruin without touching an upper barrier a. In line with this, the study demonstrates that the described Lévy risk process can essentially be replaced with a simpler risk process in which both premiums and claims are phase-type with just few phases.