We investigate the risk control and dividend optimization problem of an insurance group in a general setting and propose an innovative semi-analytical approach to the problem. The group consists of multiple subsidiaries and is subject to exogenous default risk. The default intensity is subject to the contagious effect. The contagious effect refers to the increase in default intensities of surviving subsidiaries within the group when a default event occurs. The recursive system of Hamilton-Jacobi-Bellman variational inequalities (HJBVIs) is derived together with the verification theorem. We propose a semi-analytical approach that first finds the analytical solution in the continuation region and then the numerical solution in the risk exposure region. We further present a numerical example of a three-subsidiary insurance group to demonstrate the semi-analytical method and illustrate the recursive computation procedures that are extendible to cases with more subsidiaries.

我们研究了一般环境下保险集团的风险控制和股息优化问题，并提出了一种创新的半分析方法来解决该问题。该集团由多家子公司组成，存在外生违约风险。默认强度受传染效果影响。传染效应是指当违约事件发生时，集团内幸存子公司的违约强度增加。推导了Hamilton-Jacobi-Bellman变分不等式(HJBVI)的递归系统以及验证定理。我们提出了一种半解析方法，首先在连续区域中找到解析解，然后在风险暴露区域中找到数值解。