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Optimal dividend policy with self-exciting claims in the Gamma–Omega model

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  • Liu, Guo
  • Jin, Zhuo
  • Li, Shuanming

Abstract

In this paper, we consider the optimal dividend policy for an insurance company under a contagious insurance market, where the occurrence of a claim can trigger sequent claims. This clustering effect is modelled by a self-exciting Hawkes process where the intensity of claims depends on its historical path. In addition, we include the concept of bankruptcy to allow the insurance company to operate with a temporary negative surplus. The objective of the management is to obtain the optimal dividend strategy that maximises the expected discounted dividend payments until bankruptcy. The Hamilton–Jacobi–Bellman variational inequalities (HJBVIs) are derived rigorously. When claim sizes follow exponential distributions and the bankruptcy rate is a positive constant, the value function can be obtained based on the Gerber–Shiu penalty function and the optimal dividend barrier can be solved numerically. Finally, numerical examples are demonstrated to show the impact of key parameters on the optimal dividend strategy.

Suggested Citation

  • Liu, Guo & Jin, Zhuo & Li, Shuanming, 2024. "Optimal dividend policy with self-exciting claims in the Gamma–Omega model," Finance Research Letters, Elsevier, vol. 69(PA).
    • Handle: RePEc:eee:finlet:v:69:y:2024:i:pa:s1544612324011917
    DOI: 10.1016/j.frl.2024.106162
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    References listed on IDEAS

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    1. 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.
    2. Cao, Jingyi & Landriault, David & Li, Bin, 2020. "Optimal reinsurance-investment strategy for a dynamic contagion claim model," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 206-215.
    3. Yang, Chen & Sendova, Kristina P. & Li, Zhong, 2020. "Parisian ruin with a threshold dividend strategy under the dual Lévy risk model," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 135-150.
    4. Lin, X. Sheldon & Sendova, Kristina P., 2008. "The compound Poisson risk model with multiple thresholds," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 617-627, April.
    5. Shanshan Liu & Zhaoyang Liu & Guoxin Liu, 2023. "Optimal dividend strategy for the dual model with surplus-dependent expense," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(3), pages 543-566, February.
    6. Yacine Aït-Sahalia & Thomas Robert Hurd, 2015. "Portfolio Choice in Markets with Contagion," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 14(1), pages 1-28.
    7. Liu, Guo & Jin, Zhuo & Li, Shuanming, 2021. "Optimal investment, consumption, and life insurance strategies under a mutual-exciting contagious market," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 508-524.
    8. Julia Eisenberg & Zbigniew Palmowski, 2021. "Optimal Dividends Paid in a Foreign Currency for a Lévy Insurance Risk Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 25(3), pages 417-437, July.
    9. Xiaowen Zhou, 2005. "On a Classical Risk Model with a Constant Dividend Barrier," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(4), pages 95-108.
    10. Lin, X.Sheldon & Pavlova, Kristina P., 2006. "The compound Poisson risk model with a threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 57-80, February.
    11. Benjamin Avanzi & Hayden Lau & Bernard Wong, 2021. "Optimal periodic dividend strategies for spectrally negative Lévy processes with fixed transaction costs," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2021(8), pages 645-670, September.
    12. Pablo Azcue & Nora Muler, 2010. "Optimal investment policy and dividend payment strategy in an insurance company," Papers 1010.4988, arXiv.org.
    13. Cui, Zhenyu & Nguyen, Duy, 2016. "Omega diffusion risk model with surplus-dependent tax and capital injections," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 150-161.
    14. Hans Gerber & Elias Shiu, 2006. "On Optimal Dividend Strategies In The Compound Poisson Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 76-93.
    15. Pius Babuna & Xiaohua Yang & Amatus Gyilbag & Doris Abra Awudi & David Ngmenbelle & Dehui Bian, 2020. "The Impact of COVID-19 on the Insurance Industry," IJERPH, MDPI, vol. 17(16), pages 1-14, August.
    16. Aït-Sahalia, Yacine & Cacho-Diaz, Julio & Laeven, Roger J.A., 2015. "Modeling financial contagion using mutually exciting jump processes," Journal of Financial Economics, Elsevier, vol. 117(3), pages 585-606.
    17. Dassios, Angelos & Zhao, Hongbiao, 2012. "Ruin by dynamic contagion claims," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 93-106.
    18. Zhuo Jin & Zuo Quan Xu & Bin Zou, 2022. "A perturbation approach to optimal investment, liability ratio, and dividend strategies," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2022(2), pages 165-188, February.
    19. Albrecher, Hansjörg & Lautscham, Volkmar, 2013. "From Ruin To Bankruptcy For Compound Poisson Surplus Processes," ASTIN Bulletin, Cambridge University Press, vol. 43(2), pages 213-243, May.
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    More about this item

    Keywords

    Dynamic programming; Self-exciting Hawkes process; Gamma–Omega model; Optimal dividend strategy;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G35 - Financial Economics - - Corporate Finance and Governance - - - Payout Policy

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