Research

I am a mathematical researcher specializing in the Mathematical and Stochastic Modelling of Decentralized Finance (DeFi). My work bridges rigorous Mathematical Finance and Applied Probability with Data Science to analyze and optimize the rapidly evolving DeFi ecosystem. My primary focus is on developing sophisticated models for Automated Market Makers (AMMs), contributing to both the theoretical understanding and the practical applications that will shape the future of finance.

Current Research Areas

My current research program is focused on deriving robust analytical and computational frameworks for decentralized financial systems:

• Stochastic Control and Game Theory in AMMs:
  • Arbitrage Dynamics: Investigating the non-myopic strategic interaction between arbitrageurs and AMMs, framed as a stochastic control/game, to characterize the equilibrium price and liquidity dynamics.
  • Optimal LP Strategy: Solving the Liquidity Provider’s dynamic liquidity provision strategy, which involves optimal control problems under the constraints of singular processes.
• Liquidity Modelling and Pricing:
  • Decentralized Liquidity: Developing a novel mathematical framework to model decentralized exchange liquidity dynamics in continuous time, focusing on the rigorous formulation of the evolving liquidity surface.
  • Pricing Liquidity: Relating liquidity provision to classical option pricing theory to build a practical fair fee mechanism through data-driven approaches. This aims to quantify the cost and risk of providing liquidity.
• Applied AI in Decentralized/Quantitative Finance:
  • Market Microstructure: Analyzing blockchain data to identify and model unique patterns in Web3** using techniques from data science.
  • Financial Optimization/Planning: Applying advanced machine learning, such as Distributional Reinforcement Learning (DRL) and World Models, to build robust market-making strategies that explicitly manage the heavy-tailed, non-Gaussian risks inherent in decentralized markets.

Publications

• A. Christian Silva, Shen-Ning Tung, Wei-Ru Chen. Stylized facts in Web3. Frontiers of Mathematical Finance, 2024, 3(4): 572-609. doi: 10.3934/fmf.2024021
• Joseph Najnudel, Shen-Ning Tung, Kazutoshi Yamazaki, Ju-Yi Yen. An arbitrage driven price dynamics of Automated Market Makers in the presence of fees. Frontiers of Mathematical Finance, 2024, 3(4): 560-571. doi: 10.3934/fmf.2024018
• Tung, SN. On the automorphy of 2-dimensional potentially semistable deformation rings of $G_{\mathbb{Q}_p}$. Algebra & Number Theory, 15(9), 2173–2194 (2021). doi: 10.2140/ant.2021.15.2173
• Tung, SN. On the modularity of 2-adic potentially semi-stable deformation rings. Math. Z. 298, 107–159 (2021). https://doi.org/10.1007/s00209-020-02588-4
• Paškūnas V, Tung S-N. Finiteness properties of the category of mod p representations of $\textrm{GL}_2 (\mathbb{Q}_p)$. Forum of Mathematics, Sigma. 2021;9:e80. doi:10.1017/fms.2021.72

Preprints

• Lee, C. Y., Tung, S. N., & Wang, T. H. (2024). Growth rate of liquidity provider’s wealth in G3Ms. arXiv preprint arXiv:2403.18177. (Submitted)
• Tung, S. N., & Wang, T. H. (2024). A mathematical framework for modelling CLMM dynamics in continuous time. arXiv preprint arXiv:2412.18580. (Submitted)
• Risk, J., Tung, S. N., & Wang, T. H. (2025). Dynamics of Liquidity Surfaces in Uniswap v3 arXiv preprint arXiv:2509.05013.