报告题目：How to construct a large scale optimal valid correlation matrix?

报 告 人：孙德锋教授

时    间：2020年11月19日（星期四）20:00-21:30

腾讯会议：176798696

报告人简介：

孙德锋，香港理工大学应用数学系优化和运筹研究的讲座教授，系主任。现任香港数学会会长，2020年当选SIAM会士。曾任新加坡国立大学数学系教授，新加坡国立大学风险管理研究所副所长。主要研究兴趣包括：稀疏优化、矩阵优化、高维统计优化、二阶变分分析和风险管理与计算金融等。编制了许多大规模复杂优化问题的软件，其中包括：通用的大规模半正定规划软件SDPNAL/SDPNAL+，相关矩阵校准的程序，以及最新的适用于各种各样的统计回归模型的软件包Lasso NAL。2018年因在计算数学规划上的杰出贡献，荣获国际数学规划Beale-Orchard-Hays奖。现任Mathematical Programming Series A，SIAM J. on Optimization，中国科学-数学，J. of the Operations Research Society of China，J. of Computational Mathematics的编委。曾担任Asian-Pacific J. Operational Research主编、Mathematical Programming Series B编委。

报告摘要：In finance, risk management, and many other areas, one often has to deal with invalid correlation matrices. Mathematically, a given symmetric matrix is an invalid correlation matrix if and only if its smallest eigenvalue is negative assuming that all its diagonal entries are ones. The question is how to construct a reasonably good correlation matrix from the given invalid one. Statistically, one could argue that such an invalid correlation matrix is not properly formulated and one should use better statistical methods to reconstruct a valid one. However, in practice, it is more often than not that the reformulated correlation matrix contains quite a number of negative eigen-values albeit of small magnitude. There are a number of reasons contributing to this phenomenon: insufficient/ missing raw data, non-synchronous data, human factors, and so on. In this talk we aim to construct an optimal valid correlation matrix of dimensions up to 10,000 by 10,000 from the observed one by using modern non-smooth optimization theory, in particular, on the second order sparsity of the metric projector over the cone of symmetric and positive semi-definite matrices. Computer codes in Matlab/R/Python/C for solving the correlation matrix problems will be made available to the participants. Various extensions shall also be briefly touched.

经金学院

2020年11月17日