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On a ruin model with both interclaim times and premiums depending on claim sizes

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  • Zhong Li
  • Kristina P. Sendova

Abstract

Under the classical compound Poisson risk model and the Sparre-Andersen risk model, one crucial assumption is that the interclaim times and the claim sizes are independent. However, this assumption might be inappropriate in practice. In this paper, we consider a continuous-time risk process where the interclaim-time distribution and premium rate both depend on the size of the previous claim. Explicit solutions for the Gerber–Shiu discounted penalty function with arbitrary claim-size distribution are derived utilizing the roots of a generalized Lundberg’s equation. Applications with exponential thresholds and Kn$ K_n $-family claim sizes are presented. A numerical example is provided.

Suggested Citation

  • Zhong Li & Kristina P. Sendova, 2015. "On a ruin model with both interclaim times and premiums depending on claim sizes," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2015(3), pages 245-265, April.
    • Handle: RePEc:taf:sactxx:v:2015:y:2015:i:3:p:245-265
    DOI: 10.1080/03461238.2013.811096
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