“Wir müssen wissen, wir werden wissen.” ― David Hilbert
Research Interests
- Mathematical Finance, Rough Volatility and Computational Finance
- Stochastic Analysis and Stochastic (Partial) Differential Equations
- Rough analysis and its applications
Research Projects
On the Rough and Quadratic Rough Heston Model
Supervisor: Dr. Christian Bayer
April 2025 — December 2025, WIAS and TU Berlin
This project is the topic of my master thesis. For more details, please refer to the Theses section below.
Lower Bound for Disconnection of Vacant Set in Loop Percolation
Supervisor: Prof. Dr. Maximilian Nitzschner
June 2023 — May 2024, HKUST
The principal aim of this project is to derive asymptotic lower on the probability that in a certain model of random walk loops on the integer lattice, a macroscopic set is disconnected from infinity by the trace of the loops. We further study the large deviations of the occupation-time field for the loop soup and characterize its supercritical behavior.
Publications and Preprints
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Theses
- (Master’s Degree Thesis) Second-order Weak Schemes and Error Bounds for Rough Heston and Quadratic Rough Heston Models, supervised by Dr. Christian Bayer, Winter 2026. [PDF] [Slides]
In this thesis, I mainly investigate the Rough and Quadratic Rough Heston Model. I proved that the weak scheme introduced by Bayer and Breneis indeed achieves the second-order weak rate. I also extended the PPDE method by developing Malliavin calculus framework for a broader class of SVEs, which allows us to obtain the path-dependent Feynman–Kac equation and the functional Itô formula, and thereby derived the error bound for the Quadratic Rough Heston model. Besides, an efficient weak scheme for simulating the quadratic rough Heston model is also proposed.
- (Bachelor’s Degree Thesis) Moderate Deviation of Gaussian Fluctuations for Coulomb Gases at Any Temperature, supervised by Prof. Dr. Fuqing Gao, Winter 2023. [PDF] [Slides]
In this thesis, I study and introduce the transport-based method proposed by Prof. Serfaty, which is used for obtaining the free energy expansion of Gaussian fluctuation of Coulmob gas in 2020. Then I make use of it to establish moderate deviation principle for Gaussian fluctuation of d-dim Coulomb gases with d ≥ 2.