中央财经大学孟辉：非线性脉冲再保险注资问题

　　中央财经大学中国精算研究院孟辉老师作了一场题为“Nonlinear impulse capital injections problem with reinsurance(非线性脉冲再保险注资问题)”的讲座。中央财经大学中国精算研究院下设三个研究中心：保险精算与风险管理研究中心、金融风险监测与控制研究中心和社会保障精算研究中心。在职研究生讲座的主要内容是：

　　假设两家保险公司参与再保险条约，双方保险公司和两个再保险公司采用方差保费原理。基于上述跳风险模型，我们采用扩散近似风险过程对保险公司的资产模型再保险。为了避免破产，保险公司将获得资本注入，我们假设每注资不超过某一定$ D>0$少，而且它也将招致一些固定的交易成本和比例税，即冲动注射用约束。对于扩散模型，我们研究了最小的期望折扣非线性注资。采用汉密尔顿 - 雅可比 - 贝尔曼方法，我们给出了价值函数和最优控制策略，明确的解决方案。最后，参数对最优结果的影响，我们也给数值分析。

　　原文：Assume that two reinsurers participate in a reinsurance treaty, and both the insurer and two reinsurers adopt the variance premium principle. Based on the above jump risk model, we use the diffusion approximation risk process to model the assets of insurance company with reinsurance. To avoid bankruptcy, the insurance company will receive capital injections, we assume that each capital injection is not less than a certain constant $d>0$, and it also will incurs some fixed transaction costs and proportional taxes, i.e., impulse injections with constraint. For the diffusion model, we study the minimum of the expected discounted nonlinear capital injection. Using Hamilton-Jacobi-Bellman method, we give explicit solutions for the value function and the optimal control strategy. Finally, for the influence of parameters on the optimal results, we also give numerical analysis.