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Absolute ruin in the compound Poisson risk model with constant dividend barrier

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  • Yuan, Haili
  • Hu, Yijun

Abstract

We investigate the absolute ruin in the compound Poisson risk model with nonnegative interest and a constant dividend barrier. An integro-differential equation satisfied by the absolute ruin probability, the distribution and moments of deficit at the time to absolute ruin is derived. In the case of exponential individual claim, the explicit expressions are given. Finally, by a "renewal" argument, which is different from the martingale approach, an integro-differential equation satisfied by the conditional probability of recovery is derived, based on which the probability of recovery is formulated. In the case of exponential individual claim, the explicit expression for the probability of recovery is also given.

Suggested Citation

  • Yuan, Haili & Hu, Yijun, 2008. "Absolute ruin in the compound Poisson risk model with constant dividend barrier," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2086-2094, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:14:p:2086-2094
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    References listed on IDEAS

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    7. Sheldon Lin, X. & E. Willmot, Gordon & Drekic, Steve, 2003. "The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 551-566, December.
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    Cited by:

    1. Jun Cai & Hailiang Yang, 2014. "On the decomposition of the absolute ruin probability in a perturbed compound Poisson surplus process with debit interest," Annals of Operations Research, Springer, vol. 212(1), pages 61-77, January.
    2. Li, Manman & Liu, Zaiming, 2012. "Regulated absolute ruin problem with interest structure and linear dividend barrier," Economic Modelling, Elsevier, vol. 29(5), pages 1786-1792.
    3. Yu, Wenguang, 2013. "Some results on absolute ruin in the perturbed insurance risk model with investment and debit interests," Economic Modelling, Elsevier, vol. 31(C), pages 625-634.

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