I help students with a mathematics background find their way into interdisciplinary fields such as quantitative finance, data science, and operations research: connecting their mathematical training to questions in these fields, identifying the additional knowledge and skills those questions require, and developing a direction that reflects their own interests.
I am looking for students and collaborators with interests in stochastic control / mathematical finance, machine learning / deep learning, quantitative research or algorithmic trading, or decentralized finance (DeFi). Most projects are in active early development, so there is genuine room to shape the direction. Feel free to reach out if any of the areas below interest you.
Current Research Groups
Automated Market Makers (AMMs): The mathematical design of decentralized exchanges — how liquidity evolves across prices, what a liquidity position is worth, and how providers and protocols should set liquidity and trading rules. Projects range from stochastic control and game theory to JAX-based simulation and self-supervised regime detection.
Prediction Markets: Pricing and funding event contracts, and learning methods evaluated by how well they inform liquidity decisions — including world models for short-horizon Polymarket contracts and temporal graph neural networks for sports outcomes.
See the research page for the current status of each project. The regime-detection and world-model projects offer entry points for students: both combine mathematical formulation with evaluation on held-out periods.
Current Graduate Students
Chih-Yao Wu (M.S. student, 2026–present)
Graduated Theses
Wei-Ru Chen (M.S., co-advised with Yuki Chino, June 2024)
A Study of AMM Mechanisms and Liquidity Provider Rewards. (Thesis)
The thesis formalizes the trading and liquidity-provision mechanisms of Uniswap v2 and v3, constructs a price dynamic justified by empirical observation, compares liquidity providers’ expected returns with depositing assets in a bank, and presents numerical results.
Co-authored publication: A. Christian Silva, Shen-Ning Tung, and Wei-Ru Chen, Stylized facts in Web3, Frontiers of Mathematical Finance 3(4), 572–609 (2024).
Undergraduate Research Projects
2026–present: PolyWorld
Sheng-Gang Huang and Chen-Yu Wen — PolyWorld: Latent World Models for Autonomous Market Making on Prediction Markets. Undergraduate research mentees supported by an NCTS AI grant.
2025–2026 NCTS Research Program
Hai-Ching Shih — Design a better AMM.
2024 NCTS Summer Research Program
Co-advisor: A. Christian Silva. Students: Tzu-Ling Hsieh, Guan Ting Lu, Tai-Jun Lai, Mu-Chian Lin. Optimization Methods in Quantitative Trading. (Notes)
2024 Project: Predictive Modeling for Vehicle Allocation
Role: student-team mentor. Students: Shih-Bin Chen, Jie-Hong Lai, Jia-Wei Liao, Yuan-Hong Lin. Predictive Modeling for Optimized Vehicle Allocation and Routing in Postal Delivery. Best Application Award & GLORY Data Application Innovation Award (Postal Big Data Competition, 2024). (Notes)
2023–2024 NCTS Research Program
Co-advisor: Chang-Ye Tu. Students: De-Jin Huang, Chen-Chung Yang. Deep Hedging — applying deep learning to derivative hedging strategies. (Notes)
2023 Independent Project: Time Series Generation
Hua-Hsuan Shih — Sig-Wasserstein GANs for Time Series Generation. Now at Columbia MSFE, working in the energy market industry. (Repository)