“Wir müssen wissen, wir werden wissen.” ― David Hilbert

Research Interests

• Mathematical Finance, Rough Volatility, Computational Finance and Machine Learning
• Stochastic Analysis and Stochastic (Partial) Differential Equations
• Rough analysis and its applications

Research Projects

1.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.

2.On the Rough and Quadratic Rough Heston Model

Supervisor: Dr. Christian Bayer

Ongoing, WIAS and TU Berlin

In this project, we mainly investigate the Rough and Quadratic Rough Heston Model. So far, I’ve studied the weak Markovian approximation for the Rough Heston model and proved that the weak scheme introduced by Bayer and Breneis indeed achieves the second-order weak rate they didn’t establish. And I’ve also extended the PPDE method by developing Malliavin calculus for stochastic Volterra equations, which allows us to obtain the path-dependent Feynman–Kac equation and the functional Itô formula, and thereby derive the error bound for the Quadratic Rough Heston model.

Publications and Preprints

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Theses

• (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 introduced 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 the moderate deviation principle for Gaussian fluctuation of d-dimensional Coulomb gases with d ≥ 2.