Niushan Gao
Assistant Professor

Department of Mathematics

Ryerson University


Office: EPH 421

Phone: +1 (416) 979 5000 ext 2139

Email: niushan@ryerson.ca

Mailing: Department of Mathematics, Ryerson University, 350 Victoria St., Toronto, ON, Canada M5B 2K3

photo

Research Interests
  • Mathematical Finance
  • Data Analysis and Applied Statistics
  • Machine learning
Publications
  1. NEW: A refined determinantal inequality for correlation matrices
    N. Gao, A. Kirillova, Z. Tong
    submitted arXiv
  2. NEW: On local convexity in $\mathbb{L}^0$ and switching probability measures
    N. Gao, D. Leung, F. Xanthos
    submitted arXiv

  3. Surplus-invariant risk measures
    N. Gao, C. Munari
    Mathematics of Operations Research, to appear. arXiv
  4. Closedness of convex sets in Orlicz spaces with applications to dual representation of risk measures
    N. Gao, D. Leung, F. Xanthos
    Studia Mathematica 249(3), 329-347, 2019. arXiv
  5. A local Hahn-Banach theorem and its applications
    N. Gao, D. Leung, F. Xanthos
    Archiv der Mathematik 112(5), 521-529, 2019. arXiv
  6. The strong Fatou property of risk measures
    S. Chen, N. Gao, F. Xanthos
    Dependence Modeling 6(1), 183-196, 2018. arXiv
  7. Fatou property, representations, and extensions of law-invariant risk measures on general Orlicz spaces
    N. Gao, D. Leung, C. Munari, F. Xanthos
    Finance and Stochastics 22(2), 395-415, 2018. arXiv
  8. Duality for unbounded order convergence and applications
    N. Gao, D. Leung, F. Xanthos
    Positivity 22(3), 711-725, 2018. arXiv
  9. Smallest order closed sublattices and option spanning
    N. Gao, D. Leung
    Proceedings of the American Mathematical Society 146(2), 705-716, 2018. arXiv
  10. On the C-property and w*-representations of risk measures
    N. Gao, F. Xanthos
    Mathematical Finance 28(2), 748-754, 2018. arXiv
  11. Option spanning beyond Lp-models
    N. Gao, F. Xanthos
    Mathematics and Financial Economics 11(3), 383-391, 2017.arXiv
  12. Uo-convergence and its applications to Cesaro means in Banach lattices
    N. Gao, V. Troitsky, F. Xanthos
    Israel Journal of Mathematics 220(2), 649-689, 2017. arXiv
  13. Unbounded order convergence in dual spaces
    N. Gao
    Journal of Mathematical Analysis and Applications 419(1), 347-354, 2014. arXiv
  14. Unbounded order convergence and application to martingales without probability
    N. Gao, F. Xanthos
    Journal of Mathematical Analysis and Applications 415(2), 931-947, 2014. arXiv
  15. Irreducible semigroups of positive operators on Banach lattices
    N. Gao, V. Troitsky
    Linear and Multilinear Algebra 62(1), 74-95, 2014. arXiv
  16. On commuting and semi-commuting positive operators
    N. Gao
    Proceedings of the American Mathematical Society 142(8), 2733-2745, 2014. arXiv
  17. Extensions of Perron-Frobenius theory
    N. Gao
    Positivity 17(4), 965-977, 2013. arXiv
Education
  • Ph.D. in Mathematics
    Department of Mathematical and Statistical Sciences, University of Alberta, 2013
  • B.Sc. in Mathematics
    School of Mathematical Sciences, Beijing Normal University, 2008
Employment
  • Assistant Professor
    Department of Mathematics, Ryerson University, 2017.09 - present
  • PIMS Postdoctoral Fellow
    Department of Mathematics and Computer Science, University of Lethbridge, 2016.09 - 2017.08
  • Assistant Professor
    School of Mathematics, Southwest Jiaotong University, 2014.04 - 2016.08
  • Postdoctoral Fellow
    Department of Mathematical and Statistical Sciences, University of Alberta, 2013.09 - 2014.03
Writings for Teaching

Miscellaneous Notes

Professional Supervision

PhD Students

  • Shengzhong Chen (co-supervised)
    Ryerson University, Department of Mathematics, 2019.09-present
  • Hui Li (co-supervised)
    Southwest Jiaotong University, School of Mathematics, 2015.09-present

MSc Students

  • Kathleen Miao (co-supervised)
    Ryerson University, Department of Mathematics, exp. 2020
  • Cui Chen
    Ryerson University, Department of Mathematics, exp. 2020
  • Shengzhong Chen (co-supervised)
    Ryerson University, Department of Mathematics, 2019.08
  • Harjas Singh
    Ryerson University, Department of Mathematics, 2018.08
  • Yang Deng (co-supervised)
    Southwest Jiaotong University, School of Mathematics, 2016.06

Undergraduate Students

  • Sean Davis-Lee
    Ryerson University, Fall 2019-present
  • Zihao Tong
    Ryerson University, Fall 2018-Winter 2019
  • Alexandra Kirillova
    University of Toronto, Summer 2018, May 2019
Courses Taught
  • Statistics (MTH 410)
    Ryerson University, Department of Mathematics
    Winter 2020
    Winter 2019
    Winter 2018
    Winter 2016
  • Complex Analysis (MTH 640)
    Ryerson University, Department of Mathematics
    Fall 2019
    Fall 2018
  • Analysis and Probability (AM 8001, graduate)
    Ryerson University, Department of Mathematics
    Fall 2019
    Fall 2018
  • Probability and Statistics II (MTH 404)
    Ryerson University, Department of Mathematics
    Winter 2018
  • Linear Algebra (MATH 3410)
    University of Lethbridge, Department of Mathematics and Computer Science
    Spring 2017
  • Introduction to Riesz Spaces (graduate)
    Southwest Jiaotong University, School of Mathematics
    Spring 2015
  • General Topology (graduate)
    Southwest Jiaotong University, School of Mathematics
    Fall 2014
  • Real Analysis
    Southwest Jiaotong University, School of Mathematics
    Fall 2014
  • Elementary Calculus I (MATH 113)
    University of Alberta, Department of Mathematical and Statistical Sciences
    Fall 2013
    Spring 2012
  • Elementary Theorey of Interest (MATH 153)
    University of Alberta, Department of Mathematical and Statistical Sciences
    Summer 2011