Optimal Dividend Strategy for an Insurance Group with Contagious Default Risk

TL;DR

This paper investigates the optimal dividend distribution strategy for a multi-line insurance group considering contagious default risk, revealing that optimal barriers depend on default states and providing analytical solutions for two subsidiaries.

Contribution

It introduces a model incorporating contagious default risk into the optimal dividend problem and characterizes the barrier-type strategy with state-dependent thresholds.

Findings

Optimal dividend strategy is of barrier type.

Default contagion influences the optimal barriers.

Analytical solutions derived for two subsidiaries.

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.