Abstract
In this paper, the insurance company considers venture capital and risk-free investment in a constant proportion. The surplus process is perturbed by diffusion. At first, the integro-differential equations satisfied by the expected discounted dividend payments and the Gerber-Shiu function are derived. Then, the approximate solutions of the integro-differential equations are obtained through the sinc method. Finally, the numerical examples are given when the claim sizes follow different distributions. Furthermore, the errors between the explicit solution and the numerical solution are discussed in a special case.
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Acknowledgements
The authors would like to thank the editors and the anonymous reviewers for their comments and suggestions. We would like to thank Dr. Chen Xu for her help with numerical simulation.
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The project is supported by the National Natural Science Foundation of China (No. 71801085).
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Deng, Nd., Wang, Cw. & Xu, Je. The Perturbed Compound Poisson Risk Model with Proportional Investment. Acta Math. Appl. Sin. Engl. Ser. 40, 109–128 (2024). https://doi.org/10.1007/s10255-024-1102-y
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DOI: https://doi.org/10.1007/s10255-024-1102-y
Keywords
- expected discounted dividend payments
- lognormal distribution
- proportional investment
- perturbed risk model
- sinc numerical method