{"ID":2837802,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.19701","arxiv_id":"2511.19701","title":"Optimal dividend and capital injection under self-exciting claims","abstract":"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.","short_abstract":"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-injec...","url_abs":"https://arxiv.org/abs/2511.19701","url_pdf":"https://arxiv.org/pdf/2511.19701v1","authors":"[\"Paulin Aubert\",\"Etienne Chevalier\",\"Vathana Ly Vath\"]","published":"2025-11-24T21:09:10Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.PR\",\"q-fin.RM\"]","methods":"[\"Reinforcement Learning\"]","has_code":false}