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Optimal dividend strategy for an insurance group with contagious default risk

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Listed:
  • Zhuo Jin
  • Huafu Liao
  • Yue Yang
  • Xiang Yu

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.

Suggested Citation

  • Zhuo Jin & Huafu Liao & Yue Yang & Xiang Yu, 2021. "Optimal dividend strategy for an insurance group with contagious default risk," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2021(4), pages 335-361, April.
  • Handle: RePEc:taf:sactxx:v:2021:y:2021:i:4:p:335-361
    DOI: 10.1080/03461238.2020.1845231
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    Cited by:

    1. Han, Kookyoung & Choi, Jin Hyuk, 2023. "Implications of false alarms in dynamic games on cyber-security," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Qiu, Ming & Jin, Zhuo & Li, Shuanming, 2023. "Optimal risk sharing and dividend strategies under default contagion: A semi-analytical approach," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 1-23.

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