The Perturbed Compound Poisson Risk Model with Proportional Investment  

作　　者：Nai-dan Deng Chun-wei Wang Jia-en Xu 

机构地区：[1]School of Mathematics and Statistics,Henan University of Science and Technology,Luoyang,471023,China

出　　处：《Acta Mathematicae Applicatae Sinica》2024年第1期109-128,共20页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (No. 71801085)。

摘　　要：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.

关 键 词：expected discounted dividend payments lognormal distribution proportional investment perturbed risk model sinc numerical method 

分 类 号：F840[经济管理—保险] O213[理学—概率论与数理统计]