Based on the mean-variance criterion, this paper investigates the continuous-time reinsurance and investment problem. The insurer’s surplus process is assumed to follow Cramér–Lundberg model. The insurer is allowed to purchase reinsurance for reducing claim risk. The reinsurance pattern that the insurer adopts is combining proportional and excess of loss reinsurance. In addition, the insurer can invest in financial market to increase his wealth. The financial market consists of one risk-free asset and correlated risky assets. The objective is to minimize the variance of the terminal wealth under the given expected value of the terminal wealth. By applying the principle of dynamic programming, we establish a Hamilton–Jacobi–Bellman (HJB) equation. Furthermore, we derive the explicit solutions for the optimal reinsurance-investment strategy and the corresponding efficient frontier by solving the HJB equation. Finally, numerical examples are provided to illustrate how the optimal reinsurance-investment strategy changes with model parameters.

中文翻译：

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风险资产均值方差条件下的最优再保险投资问题

基于均值-方差准则，本文研究了连续时间再保险和投资问题。假定保险人的盈余过程遵循Cramér–Lundberg模型。保险人被允许购买再保险以降低索赔风险。保险公司采用的再保险模式是将比例再保险和超额损失再保险相结合。此外，保险公司可以投资金融市场以增加其财富。金融市场由一种无风险资产和相关的风险资产。目的是在给定的最终财富期望值下，最小化最终财富的方差。通过应用动态规划原理，我们建立了汉密尔顿-雅各比-贝尔曼（HJB）方程。此外，我们通过求解HJB方程，得出了最优再保险投资策略的显式解以及相应的有效边界。最后，通过数值例子说明了最优再保险投资策略如何随着模型参数的变化而变化。