Research Interests

• Financial Mathematics

• Applied Probability

• Actuarial Science    

Preprints

• Han, X. & Schied, A. (2025). Universal portfolios in continuous time: an approach in pathwise Itô calculus. arXiv:2504.11881.

• Han, X. & Schied, A. (2025). On the rate of convergence of estimating the Hurst parameter of rough stochastic volatility models. arXiv:2504.09276.

• Han, X. & Schied, A. (2023). Estimating the roughness exponent of stochastic volatility from discrete observations of the integrated variance. arXiv:2307.02582.

Publications

• Han, X. & Schied, A. (2025). Robust Faber--Schauder approximation based on discrete observations of an antiderivative.  To appear in Mathematics of Operations Research.

• Han, X. & Schied, A. (2025). The roughness exponent and its model-free estimation. Annals of Applied Probability, 35(2), 1049-1082.

• Han, X. (2024). The roughness exponent and its application in finance. Ph.D. Thesis

• Han, X. & Schied, A. (2024). A criterion for absolute continuity relative to the law of fractional Brownian motion. Electronic Communications in Probability, 29, 1-10.

• Han, X. & Schied, A. (2022). Step roots of Littlewood polynomials and the extrema of functions in the Takagi class. Mathematical Proceedings of the Cambridge Philosophical Society, 173, 591-618.

• Han, X., Schied, A. & Zhang, Z. (2022). A limit theorem for Bernoulli convolutions and the Φ-variation of functions in the Takagi class. Journal of Theoretical Probability, 35, 2853–2878.

• Han, X., Schied, A. & Zhang, Z. (2022). A probabilistic approach to the Φ-variation of classical fractal functions with critical roughness. Statistics & Probability Letters, 168, 108920.

• Han, X. (2021). A Gladyshev theorem for trifractional Brownian motion and n-th order fractional Brownian motion. Electronic Communications in Probability, 26, 1-12.