发表机构
Fujian Normal University; The Hong Kong Polytechnic University; Xi’an Jiaotong University（福建师范大学; 香港理工大学; 西安交通大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究制度切换布朗风险模型下带固定交易成本的最优再保险-分红策略，通过粘性解刻画值函数，并给出双障碍脉冲分红与反馈再保险的最优策略。
AI 中文摘要
我们考虑布朗风险模型下的最优比例再保险-分红分配问题，其中漂移系数和波动率系数均受内生制度切换影响。分红支付需承担固定交易成本。该问题被表述为一个二维随机控制问题，我们证明了值函数是带有非局部算子的相应Hamilton-Jacobi-Bellman方程的唯一粘性解。对于几乎所有参数配置，我们显式刻画了最大化直至破产时扣除交易成本后的期望总折现分红的最优策略。最优分红策略为双障碍脉冲策略，而最优再保险比例以反馈形式给出。提供了数值示例以说明最优性结果。
英文摘要
We consider a problem of optimal proportional reinsurance-dividend distribution under a Brownian risk model, where both the drift and volatility coefficients are subject to endogenous regime-switching. Dividend payments are subject to fixed transaction costs. The problem is formulated as a two-dimensional stochastic control problem, and we prove that the value function is the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation with nonlocal operator. For almost all parameter configurations, we explicitly characterize the optimal strategy that maximizes the expected total discounted dividends net of transaction costs until ruin. The optimal dividend policy is a two-barrier impulsive strategy, while the optimal reinsurance proportion is given in feedback form. Numerical examples are provided to illustrate the optimality results.
