基于最小最大鞅测度对保险公司最优投资再保险问题的研究  

MiniMax Martingale Method for Optimal Investment-reinsurance Problem in a General Insurance Company Risk Model

作　　者：周子键 陈旭 ZHOU ZiJian;CHEN Xu(School of Mathematics and Statistics,Hunan Normal University,Changsha 410081,China)

机构地区：[1]湖南师范大学数学与统计学院,长沙410081

出　　处：《应用数学学报》2021年第3期407-417,共11页Acta Mathematicae Applicatae Sinica

基　　金：湖南省自然科学基金项目(2018JJ3328);湖南省教育厅重点项目(19A294)资助.

摘　　要：本文研究既拥有保险公司又拥有再保险公司的大型保险机构的最优管理问题.保险公司可以购买比例再保险,保险公司和再保险公司均可以购买无风险资产和风险资产,大型保险机构的目标是最大化两公司资产加权和的指数效用.通过求解最小最大鞅测度,本文给出了指数效用函数对应的最优策略的精确解.In this paper,we employ the MiniMax martingale measure to study the optimal management problem for a general insurance company which holds shares of an insurance company and a reinsurance company.The insurer can purchase proportional reinsurance,and both the insurer and the reinsurer can invest in a risk-free asset and a risky asset.The objective of the general insurance company is to maximize the expected exponential utility of the weighted sum of the insurance company’s and reinsurance company’s terminal wealth.We obtain the explicit solutions of optimal strategies for exponential utility function.

关 键 词：比例再保险策略 最小最大鞅测度 投资 再保险 

分 类 号：O211.6[理学—概率论与数理统计]