In this paper, we are interested in the optimal investment and reinsurance strategies of an insurer who wishes to maximize the expected power utility of its terminal wealth on finite time horizon. We are also interested in the problem of maximizing the growth rate of expected power utility per unit time on the infinite time horizon. The risk process of the insurer is described by an approximation of the classical Cramér–Lundberg process. The insurer invests in a market consisting of a bank account and multiple risky assets. The mean returns of the risky assets depend linearly on economic factors that are formulated as the solutions of linear stochastic differential equations. With this setting, Hamilton–Jacobi–Bellman equations that are derived via a dynamic programming approach have explicit solution obtained by solving a matrix Riccati equation. Hence, the optimal investment and reinsurance strategies can be constructed explicitly. Finally, we present some numerical results related to properties of our optimal strategy and the ruin probability using the optimal strategy.

在本文中，我们感兴趣的是保险公司的最优投资和再保险策略，该保险公司希望在有限的时间范围内最大化其终端财富的预期电力效用。我们还对在无限时间范围内最大化每单位时间预期电力效用增长率的问题感兴趣。保险公司的风险过程通过经典 Cramér-Lundberg 过程的近似来描述。保险公司投资于由银行账户和多种风险资产组成的市场。风险资产的平均回报线性取决于经济因素，这些经济因素被表述为线性随机微分方程的解。在此设置下，通过动态规划方法导出的 Hamilton-Jacobi-Bellman 方程具有通过求解矩阵 Riccati 方程获得的显式解。因此，可以明确构建最优投资和再保险策略。最后，我们提出了一些与我们的最优策略的属性和使用最优策略的破产概率相关的数值结果。