活动时间：2026-09-21 15:00
活动地点：2号学院楼2432室
主讲人：周晨
主讲人简介：
Prof. Chen Zhou is Professor of Mathematical Statistics and Risk Management at Erasmus University Rotterdam. His research focuses on extreme value statistics and quantitative risk management. His statistical work appears in Annals of Statistics, Journal of the Royal Statistical Society (Series B), Journal of American Statistical Association, Biometrika, among others. In addition, his research spans to the field of finance and economics, and has been published in leading journals including Journal of Finance and Journal of Financial and Quantitative Analysis. Chen Zhou serves as the Area Editor of Economics, Finance and Insurance at the journal Extremes. He received his PhD (2008) from Erasmus University Rotterdam, after completing his Bachelor (2001) and Master (2003) degrees at Peking University.
内容摘要：
Extremal dependence is described by the angular law of large multivariate observations. We introduce anchored geodesic component analysis, a method for constructing interpretable low-dimensional representations of this law. The method approximates extreme directions by great subspheres through a chosen anchor, with balanced complete dependence as the default. Under a bounded sine-squared geodesic loss, the population and empirical problems reduce exactly to eigenanalysis of an anchored second-moment matrix. Scores, loadings, and explained variation describe departures from the anchor, including for face- and axis-supported angular laws. We establish consistency under oracle and rank-based standardization, an oracle central limit theorem, and bounds linking angular reconstruction error to tail-functional approximation. For daily Fama–French and Open Source Asset Pricing (OSAP) portfolio losses, ten and twelve components, respectively, explain about 90% of anchored variation and closely preserve fitted coexceedance probabilities. Conventional exposure profiles nearly attain optimal rank-five angular fit for Fama–French but leave a larger gap for OSAP portfolios sorted on liquidity and trading frictions. Residual geodesic components improve coexceedance reconstruction in both panels, showing how AGCA can assess and supplement interpretable representations of joint tail risk.
主持人：唐一苇