报告人简介：
清华大学数学科学系长聘教授,博士生导师.研究领域：概率论与随机分析,精算科学,金融数学,随机控制与优化,风险管理与保险数学,数理经济学.在Mathematical Finance, Insurance: Mathematics and Economics, Scandinavian Actuarial Journal, North American Actuarial Journal, Ann.Inst.Henri Poincaré(B) Probab.Stat., Stochastic Processes and their Applications, Journal of Functional Analysis, SIAM Journal on Control and Optimization等国际一流学术杂志上发表论文六十余篇.在最优分红与投资决策，再保险, DC(DB)养老金管理与投资,数理金融,量化风险管理,最优资产配置与消费,最优投资组合与最优控制,高度非凸(凹)非线性随机控制与优化,金融与保险领域里不确定性度量与随机稳健控制问题,局部时过程与随机微分方程等方向做出了系列原创性工作.在精算科学研究领域,梁宗霞教授及其研究团队的研究位于世界前列,取得了清华大学精算科学最新四个5年周期(2012-2016, 2013-2017, 2014-2018, 2015-2019)世界非商学院类排名中分别世界排名第三,第五,第六,第八,大陆高校及研究机构排名第一的研究成果.
报告内容：In this talk, we study a problem in the principal-agent model of two general S-shaped utilities without explicit expressions, where the two parties have different reference points. The problem is featured with a principal's participating incentive compatible constraint. It turns out to be a complicated double S-shaped utility optimization problem. We propose a new classification approach to study the optimal final asset allocation. First, it is classified into two cases: (a)One-side-loss Case in which either both parties suffer liquidation, or one gains and the other loses, or both make profit; (b) Option Case in which either both parties suffer liquidation or both make profit. Further, we demonstrate an asymptotic classification of the optimal asset allocation that the single utility maximization of the principal is the limit of the Option Case, while that of the agent is the limit of the One-side-loss Case. More importantly, we find a division reservation utility such that the optimal asset allocation belongs to the Option Case beyond it and to the One-side-loss Case below. The key factor resulting in different risk choices is the size of reservation utility. As application, we numerically visualize these results with a specific participating contract, which illustrates some novel mechanisms in asset management.
