勷勤数学•专家报告

题      目：Dynamic mean-variance problem with frictions

报  告  人：马贵元   副教授  (邀请人：杨舟 )

                                    西安交通大学

时      间：7月25日  10：30-11：30

地     点：数学院西楼二楼会议室

报告人简介:

       马贵元,现任西安交通大学经济与金融学院助理教授。吉林大学数学学士学位，复旦大学运筹学与控制论方向研究生，澳大利亚Wollongong大学金融数学博士，香港中文大学博士后。主要研究领域为动态最优交易、均衡资产定价、随机控制在经济与金融领域的应用等。目前在Finance and Stochastics、European Journal of Operational Research、Automatica、Insurance: Mathematics and Economics等国际期刊发表SSCI、SCI论文共17篇。主持国家自然科学基金青年项目一项，教育部产学合作协同育人项目1项,参与国家社科项目1项，中国建设银行横向项目2项。

摘      要：

       We study a dynamic mean–variance portfolio selection problem with return predictability and trading frictions from price impact. Applying mean-field type control theory, we provide a characterization of an equilibrium trading strategy for an investor facing stochastic investment opportunities. An explicit equilibrium strategy is derived in terms of the solution to a generalized matrix Riccati differential equation, and a sufficient condition is also provided to ensure the latter’s well-posedness. Our solution indicates that the investor should trade gradually towards a target portfolio which accounts for return predictability, price impact and time-consistency. Moreover, an asymptotic analysis around small liquidity costs shows that the investor’s target portfolio is an equilibrium portfolio without price impact in the first-order sense, and that her first-order approximated value function does not deteriorate significantly for sufficiently small liquidity costs. Finally, our numerical results demonstrate that the target portfolio is more conservative than an equilibrium portfolio without price impact.          欢迎老师、同学们参加、交流！