<p style='text-indent:20px;'>We propose the stochastic factor model of optimal investment and reinsurance of insurers where the wealth processes are described by a bank account and a risk asset for investment and a Cramér-Lundberg process for reinsurance. The optimization is obtained through maximizing the exponential utility. Owing to the claims driven by a Poisson process, the proposed optimization problem is naturally treated as a jump-diffusion control problem. Applying the dynamic programming, we have the Hamilton-Jacobi-Bellman (HJB) equations and the corresponding explicit solution for the corresponding HJB. Hence, the optimal values and optimal strategies can be obtained. Finally, in numerical analysis, we illustrate the performance of the proposed optimization according to the results of the corresponding value function. In addition, compared to the wealth process without investment, the efficiency of the proposed optimization is discussed in terms of ruin probabilities.</p>

中文翻译：

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基于对数正态随机因子模型的保险公司最优投资与再保险

<p style='text-indent:20px;'>我们提出了保险公司最优投资和再保险的随机因子模型，其中财富过程由银行账户和风险资产描述，再保险过程为Cramér-Lundberg过程. 通过最大化指数效用获得优化。由于由泊松过程驱动的声明，所提出的优化问题自然被视为跳跃扩散控制问题。应用动态规划，我们有 Hamilton-Jacobi-Bellman (HJB) 方程和相应 HJB 的相应显式解。因此，可以获得最优值和最优策略。最后，在数值分析中，我们根据相应值函数的结果说明了所提出的优化的性能。