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基于新巴塞尔协议监管下保险人的均值-方差最优投资-再保险问题

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基于新巴塞尔协议监管下保险人的均值-方差最优投资-再保险问题 毕俊娜, 李旻瀚华东师范大学统计学院 统计与数据科学前沿理论及应用教育部重点实验室 上海 200241 Optimal Mean-Variance Investment-Reinsurance Problem with Constrained Controls by the New Basel Regulations for an Insurer Jun Na BI, Min Han LIKey Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE, School of Statistics, East China Normal University, Shanghai 200241, P. R. China
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摘要本文研究了均值-方差优化准则下,保险人的最优投资和最优再保险问题.我们用一个复合泊松过程模型来拟合保险人的风险过程,保险人可以投资无风险资产和价格服从跳跃-扩散过程的风险资产.此外保险人还可以购买新的业务(如再保险).本文的限制条件为投资和再保险策略均非负,即不允许卖空风险资产,且再保险的比例系数非负.除此之外,本文还引入了新巴塞尔协议对风险资产进行监管,使用随机二次线性(linear-quadratic,LQ)控制理论推导出最优值和最优策略.对应的哈密顿-雅克比-贝尔曼(Hamilton-Jacobi-Bellman,HJB)方程不再有古典解.在粘性解的框架下,我们给出了新的验证定理,并得到有效策略(最优投资策略和最优再保险策略)的显式解和有效前沿.
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收稿日期: 2019-01-03
MR (2010):O211.9
基金资助:国家自然科学基金资助项目(11571189,11871219,11871220,11901201);111引智计划(B14019)
作者简介: 毕俊娜,E-mail:jnbi@sfs.ecnu.edu.cn;李旻瀚,E-mail:554136397@qq.com
引用本文:
毕俊娜, 李旻瀚. 基于新巴塞尔协议监管下保险人的均值-方差最优投资-再保险问题[J]. 数学学报, 2020, 63(1): 61-76. Jun Na BI, Min Han LI. Optimal Mean-Variance Investment-Reinsurance Problem with Constrained Controls by the New Basel Regulations for an Insurer. Acta Mathematica Sinica, Chinese Series, 2020, 63(1): 61-76.
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