中文摘要：

该文研究了保险公司的最优投资和比例再保险问题,其中假定保险公司的盈余过程为一个带扩散扰动的经典风险过程,假定再保险的保费按照指数保费原理来计算,这使得所研究的随机控制问题成为非线性的,该文同时考虑了最大化终端财富指数效用和最大化调节系数两类问题,并给出了最优值函数和相应的最优策略的解析表达,此外,该文还分析了再保险公司的风险厌恶和保险公司的不确定性参数对最优策略的影响.

英文摘要：

This paper studies the optimal investment and proportional reinsurance policies of an insurer whose insurance business follows a diffusion perturbed classical risk process. It is assumed that the reinsurance premium is calculated according to the exponential premium principle which makes the stochastic control problems to be nonlinear. The problems of max- imizing the adjustment coefficient and the expected exponential utility of terminal wealth are considered. In both of the problems, explicit expressions for their optimal value functions and the corresponding optimal strategies are obtained. Furthermore, the influences of the risk aversion of the reinsurance company and the uncertainty of the insurance company on the optimal strategies are analyzed.