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

Shuanming Li

Scandinavian Actuarial Journal, 2006, vol. 2006, issue 2, 73-85

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.

Date: 2006
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DOI: 10.1080/03461230600589237

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