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

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

2008-03-06

arxiv.org/abs/0803.0906v1

Mathematics

Probability

23 pages with 2 figures

Scientific paper

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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