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

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  • Zhimin Zhang
  • Hailiang Yang
  • Hu Yang

Abstract

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.

Suggested Citation

  • Zhimin Zhang & Hailiang Yang & Hu Yang, 2013. "On a Sparre Andersen risk model perturbed by a spectrally negative Lévy process," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2013(3), pages 213-239.
    • Handle: RePEc:taf:sactxx:v:2013:y:2013:i:3:p:213-239
    DOI: 10.1080/03461238.2011.599141
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