Optimal dividend strategy for an insurance group with contagious default risk

Abstract

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 default contagion is considered such that one default event may increase the default probabilities of all surviving subsidiaries. The total dividend problem for the insurance group is investigated and we find that the optimal dividend strategy is still of the barrier type. Furthermore, we show that the optimal barrier of each subsidiary is modulated by the default state. That is, how many and which subsidiaries have defaulted will determine the dividend threshold of each surviving subsidiary. These 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 verification theorem is proved. 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.

Keywords:

• Insurance group
• credit default contagion
• optimal dividend
• default-state-modulated barriers
• recursive system of HJBVIs

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

X. Yu is supported by Research Grants Council, University Grants Committee (Hong Kong Early Career Scheme) (grant number 25302116) and The Hong Kong Polytechnic University (grant number P0031417).