论文标题
一种旨在最大化所有中级资本水平的预期公用事业的最佳投资策略
An optimal investment strategy aimed at maximizing the expected utility across all intermediate capital levels
论文作者
论文摘要
这项研究调查了根据Cramer-Lundberg风险模型运营的保险公司的最佳投资问题，在这种情况下，在风险资产和无风险资产中进行投资。与其他文献相反，该文献侧重于最佳投资和/或再保险策略，以最大限度地提高特定时间范围内的终端财富的预期效用，这项工作考虑了保险公司所有中级资本水平的效用的预期价值。通过采用动态编程原则，我们证明了验证定理，以证明对汉密尔顿 - 雅各比 - 贝尔曼（HJB）方程的任何解决方案都解决了我们的优化问题。在HJB方程解决方案解决方案方面的某些规律条件下，我们确定了最佳投资策略的存在。最后，为了说明理论发现的适用性，我们提出了数值示例。
This study investigates an optimal investment problem for an insurance company operating under the Cramer-Lundberg risk model, where investments are made in both a risky asset and a risk-free asset. In contrast to other literature that focuses on optimal investment and/or reinsurance strategies to maximize the expected utility of terminal wealth within a given time horizon, this work considers the expected value of utility accumulation across all intermediate capital levels of the insurer. By employing the Dynamic Programming Principle, we prove a verification theorem, in order to show that any solution to the Hamilton-Jacobi-Bellman (HJB) equation solves our optimization problem. Subject to some regularity conditions on the solution of the HJB equation, we establish the existence of the optimal investment strategy. Finally, to illustrate the applicability of the theoretical findings, we present numerical examples.
