In this article, we assume that the insurer can purchase per‐loss reinsurance and invest its surplus in a financial market consisting of a risk‐free asset and a risky asset. It is also assumed that the investment amount of the risky asset is capped at a fixed level and that short‐selling is prohibited. Our objective is to minimize the probability of absolute ruin, and the reinsurance premium is computed according to the mean‐variance premium principle, that is, a combination of the expected‐value and variance premium principles. By solving the corresponding Hamilton–Jacobi–Bellman equation, we derive explicit expressions for the S‐shaped minimum absolute ruin function and its associated optimal reinsurance‐investment strategy. We further study the same optimization problem for a slightly modified version of absolute ruin, and the corresponding optimal results are obtained as well. To gain insights into the optimal problems, we investigate the reason for the S‐shaped value function and discover that the constraint on investment control can result in the kink of minimum absolute ruin function. Finally, some properties and numerical examples are presented to show the impact of model parameters on the optimal results.

中文翻译：

---

在均值-方差溢价原则下最大程度地减少绝对破产的可能性

在本文中，我们假设保险公司可以购买按损失再保险，并将其盈余投资到一个由无风险资产和风险资产组成的金融市场中。还假设风险资产的投资额限制在固定水平，并且禁止卖空。我们的目标是最大程度地减少绝对破产的可能性，再保险费率是根据均值方差保费原理（即期望值和方差保费原理的组合）计算的。通过求解相应的Hamilton–Jacobi–Bellman方程，我们得出S形最小绝对破产函数及其相关的最优再保险投资策略的显式表达式。我们会针对略有修改的绝对破产版本进一步研究相同的优化问题，并获得相应的最佳结果。为了深入了解最优问题，我们研究了S形价值函数的原因，并发现对投资控制的约束可能导致最小绝对破产函数的扭结。最后，通过一些性质和数值例子说明了模型参数对最优结果的影响。