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

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