On a Sparre Andersen risk model perturbed by a spectrally negative Lévy process

In this paper, we consider a Sparre Andersen risk model perturbed by a spectrally negative Lévy process (SNLP). Assuming that the interclaim times follow a Coxian distribution, we show that the Laplace transforms and defective renewal equations for the Gerber–Shiu functions can be obtained by employing the roots of a generalized Lundberg equation. When the SNLP is a combination of a Brownian motion and a compound Poisson process with exponential jumps, explicit expressions and asymptotic formulas for the Gerber–Shiu functions are obtained for exponential claim size distribution and heavy-tailed claim size distribution, respectively.