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arXiv · 0803.0906

On the ruin problem in the renewal risk processes perturbed by diffusion

Min Song
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Abstract

In this paper, we consider the perturbed renewal risk process. Systems of integro-differential equations for the Gerber-Shiu functions at ruin caused by a claim and oscillation are established, respectively. The explicit Laplase transforms of Gerber-Shiu functions are obtained, while the closed form expressions for the Gerber-Shiu functions are derived when the claim amount distribution is from the rational family. Finally, we present numerical examples intended to illustrate the main results.

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Min Song. 2008-03-06. On the ruin problem in the renewal risk processes perturbed by diffusion. https://arxiv.org/abs/0803.0906

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