毓秀讲堂 |【Brownbag Seminar预告】 No.678--张元(上海财经大学)

时 间：2026年3月27日（Fri.）

12:15 - 13:15 p.m.

地 点：同德楼111

主 讲：张元（上海财经大学金融学院）

We show that a deep neural network (DNN) trained to construct a stochastic discount factor (SDF) admits a sharp additive decomposition that separates nonlinear characteristic discovery from the pricing rule that aggregates them. The economically relevant component of this decomposition is governed by a new object, the Portfolio Tangent Kernel (PTK), which captures the features learned by the network and induces an explicit linear factor pricing representation for the SDF. In population, the PTK-implied SDF converges to a ridge-regularized version of the true SDF, with the effective strength of regularization determined by the spectral complexity of the PTK. Using U.S. equity data, we show that the PTK representation delivers large and statistically significant performance gains, while its spectral complexity has risen sharply—by roughly a factor of six since the early 2000s—imposing increasingly tight limits on finite-sample pricing performance.

Yuan Zhang is an Associate Professor of Finance at Shanghai University of Finance and Economics. His research spans asset pricing, financial intermediation, and machine learning in financial markets. He has published in the *Review of Financial Studies* and is currently developing AI-driven methods for factor modeling and portfolio optimization, including work on benchmarking large language models in quantitative finance (ICLR 2026). He received his Ph.D. from the Swiss Finance Institute@EPFL and was a visiting Ph.D. student at MIT Sloan.