Optimal dividend and capital injection under self-exciting claims
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912730353500160 |
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| author | Aubert, Paulin Chevalier, Etienne Vath, Vathana Ly |
| author_facet | Aubert, Paulin Chevalier, Etienne Vath, Vathana Ly |
| contents | In this paper, we study an optimal dividend and capital-injection problem in a Cramér--Lundberg model where claim arrivals follow a Hawkes process, capturing clustering effects often observed in insurance portfolios. We establish key analytical properties of the value function and characterise the optimal capital-injection strategy through an explicit threshold. We also show that the value function is the unique viscosity solution of the associated HJB variational inequality. For numerical purposes, we first compute a benchmark solution via a monotone finite-difference scheme with Howard's policy iteration. We then develop a reinforcement learning approach based on policy-gradient and actor-critic methods. The learned strategies closely match the PDE benchmark and remain stable across initial conditions. The results highlight the relevance of policy-gradient techniques for dividend optimisation under self-exciting claim dynamics and point toward scalable methods for higher-dimensional extensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19701 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal dividend and capital injection under self-exciting claims Aubert, Paulin Chevalier, Etienne Vath, Vathana Ly Optimization and Control Probability Risk Management In this paper, we study an optimal dividend and capital-injection problem in a Cramér--Lundberg model where claim arrivals follow a Hawkes process, capturing clustering effects often observed in insurance portfolios. We establish key analytical properties of the value function and characterise the optimal capital-injection strategy through an explicit threshold. We also show that the value function is the unique viscosity solution of the associated HJB variational inequality. For numerical purposes, we first compute a benchmark solution via a monotone finite-difference scheme with Howard's policy iteration. We then develop a reinforcement learning approach based on policy-gradient and actor-critic methods. The learned strategies closely match the PDE benchmark and remain stable across initial conditions. The results highlight the relevance of policy-gradient techniques for dividend optimisation under self-exciting claim dynamics and point toward scalable methods for higher-dimensional extensions. |
| title | Optimal dividend and capital injection under self-exciting claims |
| topic | Optimization and Control Probability Risk Management |
| url | https://arxiv.org/abs/2511.19701 |