勷勤数学•专家报告

题      目：Extended Dynamic Programming Principle and Applications to Time-Inconsistent Control

报  告  人：徐玉红  教授  (邀请人：杨舟)

                                  苏州大学

时      间：11月9日  16：30-17：30

地     点：数科院西楼二楼会议室

报告人简介:

       苏州大学正高职研究员，博士生导师，仲英青年学者。师从国际著名金融数学家彭实戈院士。先后在法国西布列塔尼大学(博士后)、新加坡国立大学(研究员)、香港大学、香港理工等学校访问工作。长期从事金融工程与科技方面的研究，研究结果在《Mathematical Finance》、《Management Science》、《Quantitative Finance》、《North American Journal of Economics and Finance》等杂志发表。任中国运筹学会金融工程与风险管理分会第三、四届常务理事、中国优选法统筹法与经济数学研究会量化金融与保险分会第一、二届理事、全国工业统计研究会金融科技与大数据分会第一届理事、中国工业与应用数学协会金融工程分会青年组委员、金融数学与数据处理年会程序委员。先后主持国家自然科学基金3项、江苏省自然科学基金2项。

摘      要：

       This paper investigates an extended dynamic programming principle (DPP) for a general stochastic control problem in which the state processes are described by a forward-backward stochastic differential equation (FBSDE). A multidimensional DPP is established with auxiliary dimensions defined by a BSDE. Consequently, an extended Hamilton-Jacobi-Bellman (HJB) equation is derived. The existence and uniqueness of smooth solution and a new type of viscosity solution are investigated for this extended HJB equation. Compared to extant research on the stochastic maximum principle, the present paper is the first normal work on the partial differential equation (PDE) method for a control system with states evolving in both forward and backward manners. Interestingly, our extended DPP provides a time-consistent equilibrium solution for general time-inconsistent control problems associated with the traditional mean-variance model, risk-sensitive control and utility optimization for narrow framing investors, among others.

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