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中文摘要：
本文对索赔次数为复合Poisson—Geometric过程的风险模型，在保险公司的盈余可以投资于风险资产，以及索赔购买比例再保险的策略下，研究使得破产概率最小的最优投资和再保险策略．通过求解相应的Hamilton—Jacobi—Bellman方程，得到使得破产概率最小的最优投资和比例再保险策略，以及最小破产概率的显示表达式．
英文摘要：
In this paper,we consider an insurance company whose surplus （reserve） is modeled by a compound Poisson-Geometric risk process perturbed by a diffusion. The insurance company can invest part of the surplus in a risky asset and purchase proportional reinsurance for claims. We consider the optimization problem of minimizing the probability of ruin. By solving the corresponding Hamilton-Jacobi-Bellman equations, explicit expressions for the minimal ruin probability and the corresponding optimal strategies are obtained.
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