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The distribution of the dividend payments in the compound poisson risk model perturbed by diffusion

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  • Shuanming Li

Abstract

We consider a diffusion perturbed classical compound Poisson risk model in the presence of a constant dividend barrier. An integro-differential equation with certain boundary conditions for the n-th moment of the discounted dividend payments prior to ruin is derived and solved. Its solution can be expressed in terms of the expected discounted penalty (Gerber-Shiu) functions due to oscillation in the corresponding perturbed risk model without a barrier. When the discount factor δ is zero, we show that all the results can be expressed in terms of the non-ruin probability in the perturbed risk model without a barrier.

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  • Shuanming Li, 2006. "The distribution of the dividend payments in the compound poisson risk model perturbed by diffusion," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2006(2), pages 73-85.
    • Handle: RePEc:taf:sactxx:v:2006:y:2006:i:2:p:73-85
    DOI: 10.1080/03461230600589237
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    Cited by:

    1. Zan Yu & Lianzeng Zhang, 2024. "Computing the Gerber-Shiu function with interest and a constant dividend barrier by physics-informed neural networks," Papers 2401.04378, arXiv.org.
    2. Zhang, Zhikun & Dai, Min & Wang, Xiangjun, 2023. "Statistical inference for mixed jump processes by Markov switching model with application to identify seismicity levels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).

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