Optimal Dividend Strategy for An Insurance Group with Contagious Default Risk
Abstract
This paper studies the optimal dividend for a multiline insurance group, in which each subsidiary runs a product line and is exposed to some external credit default risk. The external default contagion is considered in the sense that one default event can affect the default probabilities of all surviving subsidiaries. The total dividend problem is formulated for the insurance group and we reveal for the first time that the optimal singular dividend strategy is still of the barrier type. Furthermore, we show that the optimal barrier for each subsidiary is modulated by the current default state, namely how many and which subsidiaries have defaulted will determine the dividend threshold for each surviving subsidiary. These interesting conclusions are based on our analysis of the associated recursive system of HamiltonJacobiBellman variational inequalities (HJBVIs), which is new to the literature. The existence of the classical solution is established and the rigorous proof of the verification theorem is provided. For the case of two subsidiaries, the value function and optimal barriers for each subsidiary are explicitly constructed. Some numerical examples are also presented to illustrate the economic insights.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 arXiv:
 arXiv:1909.09511
 Bibcode:
 2019arXiv190909511J
 Keywords:

 Quantitative Finance  Risk Management;
 Mathematics  Optimization and Control
 EPrint:
 Keywords: Insurance group, external default contagion, optimal dividend, reflection control, defaultstatemodulated barriers, recursive system of HJBVIs