Manuscript, 2025
A comparative study of hybrid LSTM-GARCH frameworks for realized-volatility forecasting.
Recommended citation: Yue Yihua, Rong Jia, Lv Zimeng, Xiao Tongren, and Li Ke. "A Comparative Study of Hybrid LSTM Frameworks for Volatility Forecasting in the NASDAQ-100 and S&P 500 Markets." Manuscript, 2025.
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Work in progress, 2026
A probabilistic world-model formulation for multi-asset realized-volatility forecasting.
Recommended citation: Tongren Xiao. "Anchor-Conditioned Probabilistic World Models for Multi-Asset Realized-Volatility Paths." Work in progress, 2026.
Manuscript, 2026
A proof-oriented study of Graham positivity for quantum double Schubert polynomials.
Recommended citation: Tongren Xiao and Yihua Yue. "Graham Positivity of Quantum Double Schubert Polynomials." Manuscript, 2026.
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Published in Research note, 2026
Research on the Goreinov-Tyrtyshnikov-Zamarashkin conjecture concerning well-conditioned submatrices of orthonormal frames.
Recommended citation: Tongren Xiao. "Submatrix Selection for Matrices with Orthonormal Columns." Research note, 2026.
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Published in Manuscript; arXiv preprint forthcoming, 2026
A geometric analog forecasting framework for realized volatility based on similarity between historical volatility paths.
Recommended citation: Tongren Xiao and Shuhang Chen. "Shape Is Useful: Geometric Analog Forecasting of Realized Volatility." Manuscript, 2026; arXiv preprint forthcoming.
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