I am a researcher working at the intersection of digital finance, mathematical modeling, and AI. My work combines rigorous mathematical tools with modern machine learning to understand and improve how digital financial markets are designed and operated. The central question is: can we replace hand-crafted rules and assumptions in market design with systems that learn directly from data?
This work spans two connected areas, both grounded in representation learning — systems that learn structure from data.
Automated Market Makers (AMMs)
Redesigning decentralized exchange protocols to better protect passive liquidity providers (LPs) against Loss-Versus-Rebalancing (LVR), the quiet drain caused by informed traders exploiting price gaps. (AMM challenge · Prop AMM challenge)
- Multi-AMM simulation in JAX — high-speed, fully compiled simulator for RL-based fee and pool design experiments across competing pools.
- Single-period LP pricing (Glosten–Milgrom) — optimal price distribution for a LP facing a mix of informed and uninformed traders; reveals a sharp threshold where quotes shift abruptly to defensive wide spreads.
- N-player LP competition — Nash equilibrium characterization of competing LPs; in equilibrium, liquidity must be spread continuously and profit margins vanish as N grows.
- Stackelberg arbitrage game — two-level game between pool operator and competing arbitrageurs, with conditions guaranteeing a unique stable equilibrium.
- am-AMM continuous-time control — stochastic optimal control for auction-managed AMMs; closed-form solutions for optimal fees and rental policies. (am-AMM original paper)
- P&L-aware regime detection (SSRD) — neural encoder that clusters market states by LP profitability impact rather than statistical similarity.
Prediction Markets & High-Frequency Dynamics
Building learning systems that extract actionable signals directly from raw market data, bypassing brittle hand-engineered features. (Prediction market challenge)
- Short-term binary options via JEPA — world model for 5–15 min Polymarket contracts; learns compact latent representations of limit order book states and plans quoting strategies in latent space rather than predicting raw prices. (LeCun on JEPA and world models: part I · part II)
- Sports betting via temporal GNNs — graph neural network over historical match results that routes information across international competitions to calibrate team strength, with uncertainty widening at season boundaries and a shared backbone for multi-proposition prediction.
Preprints
Pricing and hedging for liquidity provision in Constant Function Market Making. Risk, J., Tung, S. N., & Wang, T. H. arXiv:2603.01344 (submitted).
Dynamics of liquidity surfaces in Uniswap v3. Risk, J., Tung, S. N., & Wang, T. H. arXiv:2509.05013 (submitted).
Publications
DeFi & Mathematical Finance
A mathematical framework for modelling CLMM dynamics in continuous time. Tung, S. N., & Wang, T. H. Digital Finance (accepted). arXiv:2412.18580
Growth rate of liquidity provider’s wealth in G3Ms. Lee, C. Y., Tung, S.-N., & Wang, T.-H. Applied Mathematical Finance, 32(6), 379–422 (2026).
Stylized facts in Web3. Silva, A. C., Tung, S.-N., & Chen, W.-R. Frontiers of Mathematical Finance, 3(4), 572–609 (2024).
An arbitrage driven price dynamics of Automated Market Makers in the presence of fees. Najnudel, J., Tung, S.-N., Yamazaki, K., & Yen, J.-Y. Frontiers of Mathematical Finance, 3(4), 560–571 (2024).
Number Theory
On the automorphy of 2-dimensional potentially semistable deformation rings of $G_{\mathbb{Q}_p}$. Tung, S.-N. Algebra & Number Theory, 15(9), 2173–2194 (2021).
On the modularity of 2-adic potentially semi-stable deformation rings. Tung, S.-N. Mathematische Zeitschrift, 298, 107–159 (2021).
Finiteness properties of the category of mod p representations of $\mathrm{GL}_2(\mathbb{Q}_p)$. Paškūnas, V., & Tung, S.-N. Forum of Mathematics, Sigma, 9, e80 (2021).