Ting-Kam Leonard Wong

Associate Professor

Department of Statistical Sciences
University of Toronto
St George office: Room 9114, Hydro Building (OPG)

Department of Computer and Mathematical Sciences
University of Toronto Scarborough
UTSC office: Room 4040, Sam Ibrahim Building (IA)

E-mail: tkl.wong"at"utoronto.ca

Research

Research interests:

Mathematical finance, probability, optimal transport, information geometry, and their applications.
Google schole profile:
arXiv profile:

Featured recent work:

This figure illustrutes on the simplex the dual and primal displacement interpolations between probability distributions which are key components of the geometry of the Bregman-Wasserstein divergence. Image credit: Amanjit Singh Kainth.


Evolution of the capital distribution curve of the US equity market. The long-term stability of this object is of significant theoretical and practical interest. In this paper we conduct a comprehsive study of several macroscopic properties of the market motivated by stochastic portfolio theory.

Funding:

My research is partially supported by NSERC Discovery Grant (RGPIN-2019-04419).
In 2020 I was happy to receive a Connaught New Researcher Award.
I also gratefully acknowledge support from the Data Science Institute Seed Funding for Methodologists (2022).

PhD students:

• Elijah French (Statistics, co-supervised by Sebastian Jaimungal)
  
• Madhu Gunasingam (Statistics)
  
• Amanjit Kainth (Computer Science, co-supervised by Frank Rudzicz)
  
• (Defended 2023) Steven Campbell (Statistics, co-supervised by Yuchong Zhang)
  Thesis: Optimization Problems in Model-Free Stochastic Portfolio Theory and Sequential Testing Games

Publications:

• 28. Maximum likelihood estimation for the λ-exponential family
  With Xiwei Tian, Jiaowen Yang and Jun Zhang.
  Preprint (2025).
  Manuscript available upon request.
  
• 27. On the Wasserstein alignment problem
  With Soumik Pal and Bodhisattva Sen.
  Preprint (2025).
  [arXiv]
  
• 26. Macroscopic properties of equity markets: stylized facts and portfolio performance
  With Steven Campbell and Qien Song.
  Preprint (2024).
  [arXiv] [code]
  
• 25. JKO schemes with general costs
  With Cale Rankin.
  Preprint (2024).
  [arXiv]
  
• 24. Bregman-Wasserstein divergence: geometry and applications
  With Amanjit Singh Kainth and Cale Rankin.
  Preprint (2023).
  [arXiv] [code]
  
• 23. Adapted optimal transport between Gaussian processes in discrete time
  With Madhu Gunasingam.
  Electronic Communications in Probability (2025).
  [journal]
  
• 22. Efficient convex PCA with applications to Wasserstein geodesic PCA and ranked data
  With Steven Campbell.
  Journal of Computational and Graphical Statistics (2024).
  [journal] [arXiv] [codes]
  
• 21. Conformal mirror descent with logarithmic divergences
  With Amanjit Singh Kainth and Frank Rudzicz.
  Information Geometry (2022).
  [journal] [code]
  
• 20. Tsallis and Rényi deformations linked via a new λ-duality
  With Jun Zhang.
  IEEE Transactions on Information Theory (2022).
  [journal]
• 19. Functional portfolio optimization in stochastic portfolio theory
  With Steven Campbell.
  SIAM Journal on Financial Mathematics (2022).
  [journal] [codes]
• 18. λ-deformation: A canonical framework for statistical manifolds of constant curvature
  With Jun Zhang.
  Entropy (2022).
  [journal]
• 17. Random concave functions
  With Peter Baxendale.
  Annals of Applied Probability (2022).
  [journal]
• 16. λ-deformed probability families with subtractive and divisive normalizations
  With Jun Zhang.
  Handbook of Statistics (2021).
  [book chapter]
• 15. Pseudo-Riemannian geometry encodes information geometry in optimal transport
  With Jiaowen Yang.
  Information Geometry (2021).
  [journal]
• 14. Projections with logarithmic divergences
  With Zhixu Tao.
  Proceedings of the 5th Conference on Geometric Science of Information (2021).
  [proceeding]
• 13. On time-consistent conditional expectation under probability distortion
  With Jin Ma and Jianfeng Zhang.
  Mathematics of Operations Research (2021).
  [journal]
• 12. Multiplicative Schrödinger problem and the Dirichlet transport
  With Soumik Pal.
  Probability Theory and Related Fields (2020).
  [journal]
• 11. Scalable gradients for stochastic differential equations
  With Xuechen Li, Ricky T. Q. Chen and David Duvenaud.
  AISTATS 2020.
  [arXiv] [proceeding]
• 10. Random walks and induced Dirichlet forms on compact spaces of homogeneous type
  With Ka-Sing Lau and Shi-Lei Kong.
  In Analysis, Probability and Mathematical Physics on Fractals, World Scientific (2020).
  [book chapter]
  
• 9. Logarithmic divergence: geometry and interpretation of curvature
  With Jiaowen Yang.
  Proceedings of the 4th Conference on Geometric Science of Information (Best Paper Award) (2019).
  [proceeding]
  
• 8. Cover's universal portfolio, stochastic portfolio theory and the numeraire portfolio
  With Christa Cuchiero and Walter Schachermayer.
  Mathematical Finance (2019).
  [journal]
• 7. Information geometry in portfolio theory
  In Geometric Structures of Information, Springer (2019).
  [book chapter]
• 6. Logarithmic divergences from optimal transport and Rényi geometry
  Information Geometry (2018).
  [journal]
• 5. Exponentially concave functions and a new information geometry
  With Soumik Pal.
  The Annals of Probability (2018).
  [journal]
• 4. Random walks and induced Dirichlet forms on self-similar sets
  with Ka-Sing Lau and Shi-Lei Kong.
  Advances in Mathematics (2017).
  [journal]
• 3. The geometry of relative arbitrage
  With Soumik Pal.
  Mathematics and Financial Economics (2016).
  [journal]
• 2. Volatility harvesting in theory and practice
  With Paul Bouchey and Vassilii Nemtchinov.
  The Journal of Wealth Management (2015).
  [journal]
• 1. Optimization of relative arbitrage
  Annals of Finance (2015).
  [journal]

Other manuscripts and works

• Information geometry for the working information theorist
  With Kumar Vijay Mishra and M Ashok Kumar.
  [arXiv]
  
• Universal portfolios in stochastic portfolio theory
  [arXiv]
• Geometry and Optimization of Relative Arbitrage
  PhD Thesis (2016). University of Washington.
  [link]
• R Package. RelValAnalysis - Relative Value Analysis
  Available on [CRAN]
• Energy, entropy, and arbitrage
  With Soumik Pal.
  [arXiv]
• Boundary Theory of Random Walk and Fractal Analysis
  Mphil Thesis (2011). The Chinese University of Hong Kong.
  [link]
• Induced measures of simple random walks on Sierpinski graphs
  [arXiv]