This paper studies the optimal dividend for a multi-line insurance group, in which each subsidiary runs a product line and is exposed to some external credit risk. The credit default contagion is considered in the sense that one default event may increase the default probabilities of all surviving subsidiaries. The total dividend problem is considered for the insurance group and we reveal that the optimal singular dividend strategy is still of the barrier type. Furthermore, we show that the optimal barrier of each subsidiary is modulated by the default state, namely how many and which subsidiaries have defaulted will determine the dividend threshold of each surviving subsidiary. These interesting conclusions are based on the analysis of the associated recursive system of Hamilton-Jacobi-Bellman variational inequalities (HJBVIs). The existence of the classical solution is established and the proof of the verification theorem is provided. In the case of two subsidiaries, the value function and optimal barriers are given in analytical forms, allowing us to conclude that the optimal barrier of one subsidiary decreases if the other subsidiary defaults.

中文翻译：

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具有传染性违约风险的保险集团的最优分红策略

本文研究了多线保险集团的最优股息，其中每个子公司都经营一条产品线并面临一些外部信用风险。信用违约蔓延是在一个违约事件可能会增加所有幸存子公司的违约概率的意义上考虑的。考虑保险集团的总分红问题，我们发现最优的单一分红策略仍然是障碍型的。此外，我们表明每个子公司的最优障碍受违约状态的调节，即违约的子公司数量和违约将决定每个幸存子公司的股息阈值。这些有趣的结论是基于对 Hamilton-Jacobi-Bellman 变分不等式 (HJBVI) 相关递归系统的分析。建立了经典解的存在性，并给出了验证定理的证明。在两个子公司的情况下，价值函数和最优障碍以分析形式给出，使我们能够得出结论，如果另一个子公司违约，一个子公司的最优障碍就会减少。