Abstract: In order to study the Gerber-Shiu discounted penalty function for the compound Poisson-Geometric risk model with investment and constant barrier dividend, the defective renewal equation of the Gerber-Shiu discounted penalty function is obtained by using the method of total expectation formula. The closed form solution of the ruin probability with investment and constant barrier dividend for an insurance company is given that the premium amounts and the claim amounts follow exponential distribution. To illustrate the reasonableness of the obtained theoretical results and to give some important guidance suggestions on the management of insurance funds, the effects of the initial amount of preparation、the deviation coefficient、the amount of investment on the ruin probability are analyzed by two numerical examples.It is shown that:adequate initial reserve、lower compensation threshold and higher return on risky assets are important strategies to reduce ruin risk.

Key words: compound Poisson-Geometric process, investment, barrier dividend, Gerber-Shiu function, ruin probability

摘要： 文章考虑了复合Poisson-Geometic风险下带投资和障碍分红的Gerber-shiu函数问题,运用全期望公式得到了复合Poisson-Geometic风险下带投资和障碍分红的函数所满足的更新方程。并在指数分布的假设下,得到了带投资和障碍分红的保险公司的破产概率的显式表达,最后通过数值算例分析了风险模型的几个关键参数对破产概率的影响,验证了文章结果的合理性,同时也给保险公司的资金管理提出了指导意见。结果表明:充足的初始准备金、较低的赔付门槛、较高收益率的风险资产都是降低破产风险的重要策略。

关键词: 复合Poisson-Geometric过程, 风险投资, 障碍分红, Gerber-Shiu函数, 破产概率