This paper studies the optimal dividend for a multi-line insurance group, in which each insurance company 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 insurance companies . 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 insurance company is modulated by the current default state, namely how many and which companies have defaulted will determine the dividend threshold for each surviving company . These interesting conclusions match with observations from the real market and are based on our analysis of the associated recursive system of Hamilton-Jacobi-Bellman 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 companies , the value function and optimal barriers for each company can be explicitly constructed. Some numerical examples are also presented  .
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 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 Hamilton-Jacobi-Bellman 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 .
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insurance company
subsidiary runs a product line and
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insurance companies
subsidiaries
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insurance company
subsidiary
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companies
subsidiaries
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company
subsidiary
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match with observations from the real market and
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companies
subsidiaries
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company can be
subsidiary are
A
to illustrate the economic insights