带投资比例的扰动复合泊松风险模型

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Nai-dan Deng, Chun-wei Wang, Jia-en Xu
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引用次数: 0

摘要

在本文中,保险公司将风险投资和无风险投资的比例保持不变。盈余过程受到扩散的扰动。首先,推导出预期贴现红利支付和 Gerber-Shiu 函数所满足的微分方程。然后,通过 sinc 方法求得整微分方程的近似解。最后,举例说明了当债权规模遵循不同分布时的数值计算。此外,在一个特例中讨论了显式解和数值解之间的误差。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Perturbed Compound Poisson Risk Model with Proportional Investment

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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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
70
审稿时长
3.0 months
期刊介绍: Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.
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