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The expected discounted penalty function for two classes of risk processes perturbed by diffusion with multiple thresholds

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Listed:
  • Wuyuan Jiang

    (Hunan Institute of Science and Technology)

  • Zhaojun Yang

    (Hunan University)

Abstract

In this paper, we consider a perturbed risk model with two independent classes of risks under multiple thresholds in which both of the two inter-claim times have phase-type distributions. We obtain the integro-differential equations with boundary conditions for the expected discounted penalty function. Explicit expressions are derived if the two classes claim amount distributions both belong to the rational family.

Suggested Citation

  • Wuyuan Jiang & Zhaojun Yang, 2014. "The expected discounted penalty function for two classes of risk processes perturbed by diffusion with multiple thresholds," Indian Journal of Pure and Applied Mathematics, Springer, vol. 45(4), pages 479-495, August.
    • Handle: RePEc:spr:indpam:v:45:y:2014:i:4:d:10.1007_s13226-014-0076-5
    DOI: 10.1007/s13226-014-0076-5
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    References listed on IDEAS

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    1. Lin, X. Sheldon & Sendova, Kristina P., 2008. "The compound Poisson risk model with multiple thresholds," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 617-627, April.
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    6. Yang, Hu & Zhang, Zhimin, 2008. "Gerber-Shiu discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 984-991, June.
    7. Jiandong Ren, 2007. "The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 128-136.
    8. Jiang, Wuyuan & Yang, Zhaojun & Li, Xinping, 2012. "The discounted penalty function with multi-layer dividend strategy in the phase-type risk model," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1358-1366.
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