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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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    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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