Optimal risk sharing and dividend strategies under default contagion: A semi-analytical approach

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.