Abstract The present paper addresses the issue of choosing an optimal dynamic reinsurance policy, which is state-dependent, for an insurance company that operates under multiple insurance business lines. For each line, the Cramer–Landberg model is adopted for the risk process and one of the contracts such as Proportional reinsurance, excess-of-loss reinsurance (XL) and limited XL reinsurance (LXL) is intended for transferring a portion of the risk to the reinsurance. In the optimization method used in this paper, the survival function is maximized with respect to to the dynamic reinsurance strategies. The optimal survival function is characterized as the unique nondecreasing viscosity solution of the associated Hamilton-Jacobi-Bellman (HJB) equation with limit one at infinity. The finite difference method (FDM) has been utilized for the numerical solution of the optimal survival function and optimal dynamic reinsurance strategies and the proof for the convergence of the numerical solution to the survival probability function is provided. The findings of this paper provide insights for the insurance companies as such that based upon the lines in which they are operating, they can choose a vector of the optimal dynamic reinsurance strategies and consequently transfer some part of their risks to several reinsurers. With the numerical examples, the significance of the elicited results in reducing the probability of ruin is demonstrated in comparison with the previous findings.

中文翻译：

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多维组合中的最优动态再保险策略

摘要 本文解决了为一家在多个保险业务线下运营的保险公司选择最佳动态再保险政策的问题，该政策依赖于国家。每条线路的风险过程均采用Cramer-Landberg模型，按比例再保险、超额损失再保险（XL）和有限XL再保险（LXL）等合同之一用于转移一部分风险到再保险。在本文中使用的优化方法中，生存函数相对于动态再保险策略被最大化。最优生存函数的特征是相关联的 Hamilton-Jacobi-Bellman (HJB) 方程的唯一非递减粘度解，其极限为无穷大。有限差分法(FDM)被用于最优生存函数和最优动态再保险策略的数值解，并证明了数值解对生存概率函数的收敛性。本文的研究结果为保险公司提供了见解，因为它们可以根据其运营的线路，选择最佳动态再保险策略的向量，从而将其部分风险转移给多个再保险公司。通过数值例子，与之前的发现相比，得出的结果在降低破产概率方面的重要性得到了证明。