报告题目：Portfolio diversification and model uncertainty: a robust dynamic mean-variance approach
This talks focuses on a dynamic multi-asset mean-variance portfolio selection problem under model uncertainty. We develop a continuous time framework for taking into account ambiguity aversion about both expected return rates and correlation matrix of the assets, and for studying the join effects on portfolio diversification. The dynamic setting allows us to consider time varying ambiguity sets, which include the cases where the drift and correlation are estimated on a rolling window of historical data or when the investor takes into account learning on the ambiguity. In this context, we prove a general separation principle for the associated robust control problem, which allows us to reduce the determination of the optimal dynamic strategy to the parametric computation of the minimal risk premium function. Our results provide a justification for under-diversification, as documented in empirical studies and in the static models. Furthermore, we explicitly quantify the degree of under-diversification in terms of correlation bounds and Sharpe ratios proximities, and emphasize the different features induced by drift and correlation ambiguity. In particular, we show that an investor with a poor confidence in the expected return estimation does not hold any risky asset, and on the other hand, trades only one risky asset when the level of ambiguity on correlation matrix is large. We also provide a complete picture of the diversification for the optimal robust portfolio in the three-asset case.
主讲人简介:周超毕业于法国巴黎九大和巴黎综合理工大学，现为新加坡国立大学数学系和风险管理研究院副教授。他同时任新加坡国立大学量化金融中心主任并负责量化金融硕士项目。周超的主要研究领域包括金融数学，随机控制，深度学习方法在金融中的应用。他在《The Annals of Probability》，《The Annals of Applied Probability》、《Mathematical Finance》、《Finance and Stochastics》、《Journal of Economic Dynamics & Control》、《SIAM Journal on Control and Optimization》、《SIAM Journal on Financial Mathematics》等多个国际权威的金融数学杂志上发表论 文30余篇。