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

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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周子键, 陈旭湖南师范大学数学与统计学院, 长沙 410081 MiniMax Martingale Method for Optimal Investment-reinsurance Problem in a General Insurance Company Risk Model ZHOU ZiJian, CHEN XuSchool of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China

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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.

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收稿日期: 2019-08-26

PACS:	60J75
	91B30

基金资助: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.

引用本文:

周子键, 陈旭. 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[J]. 应用数学学报, 2021, 44(3): 407-417. ZHOU ZiJian, CHEN Xu. MiniMax Martingale Method for Optimal Investment-reinsurance Problem in a General Insurance Company Risk Model. Acta Mathematicae Applicatae Sinica, 2021, 44(3): 407-417.

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