arXiv subjects

Shen-Ning Tung

Publications and source records attributed to Shen-Ning Tung.

10 recordsLinked to original sources

arXiv2026

Pre-game paired-comparison modeling of professional League of Legends map outcomes

We build and evaluate a pre-game win-probability forecaster for individual maps (``games'') in professional \emph{League of Legends} (LoL). The proposed model is a one-stage logistic regression fit end-to-end on the win/loss log-loss: each team's exponentially-weighted moving average of past same-side results, a ridge-shrunk stable strength that is the maximum-a-posteriori estimate of a logistic mixed model, and a first-pick draft covariate, natively calibrated out of sample (walk-forward slope $0.995$). It augments a purely dynamic Bradley--Terry specification with stable team strengths. A second, independently built two-stage composite mixed model under restricted maximum likelihood (REML) and best linear unbiased prediction (BLUP) shrinkage, with Platt calibration, serves as the strongest rival the authors could build. On $5{,}135$ games across six regional leagues and three international events (2024--2026), under paired per-game Diebold--Mariano inference, the two architectures are statistically indistinguishable on every protocol and window (global holdout $0.2230$ vs.\ $0.2257$; walk-forward $0.2207$ vs.\ $0.2215$), so the simpler model is preferred on parsimony, not accuracy; both improve on the classical dynamic benchmark ($0.2351$) by a clear margin and on the static fits ($0.2301$/$0.2268$) more modestly. Against Polymarket on $928$ matched maps, the forecasts are statistically indistinguishable from the market on its own per-game contracts, with a modest market edge concentrated on cross-region Worlds and series-decider maps.

stat.AP↗

arXiv2026

Growth rate of liquidity provider's wealth in G3Ms

We study how trading fees and continuous-time arbitrage affect the profitability of liquidity providers (LPs) in Geometric Mean Market Makers (G3Ms). We use stochastic reflected diffusion processes to analyze the dynamics of a G3M model under the arbitrage-driven market. Our research focuses on calculating LP wealth and extends the findings of Tassy and White related to the constant product market maker (Uniswap v2) to a wider range of G3Ms, including Balancer. This allows us to calculate the long-term expected logarithmic growth of LP wealth, offering new insights into the complex dynamics of AMMs and their implications for LPs in decentralized finance.

q-fin.MF↗

arXiv2026

Pricing and hedging for liquidity provision in Constant Function Market Making

This paper develops a robust mathematical framework for Constant Function Market Makers (CFMMs) by transitioning from traditional token reserve analyses to a coordinate system defined by price and intrinsic liquidity. We establish a canonical parametrization of the bonding curve that ensures dimensional consistency across diverse trading functions, such as those employed by Uniswap and Balancer, and demonstrate that asset reserves and value functions exhibit a linear dependence on this intrinsic liquidity. This linear structure facilitates a streamlined approach to arbitrage-free pricing, delta hedging, and systematic risk management. By leveraging the Carr-Madan spanning formula, we characterize Impermanent Loss (IL) as a weighted strip of vanilla options, thereby defining a fine-grained implied volatility structure for liquidity profiles. Furthermore, we provide a path-dependent analysis of IL using the last-passage time. Empirical results from Uniswap v3 ETH/USDC pools and Deribit option markets confirm a volatility smile consistent with crypto-asset dynamics, validating the framework's utility in characterizing the risk-neutral fair value of liquidity provision.

q-fin.MF↗

arXiv2025

Dynamics of Liquidity Surfaces in Uniswap v3

This paper presents a comprehensive study on the empirical dynamics of Uniswap v3 liquidity, which we model as a time-tick surface, $L_t(x)$. Using a combination of functional principal component analysis (FPCA) and dynamic factor methods, we analyze three distinct pools over multiple sample periods. Our findings offer three main contributions: a statistical characterization of automated market maker liquidity, an interpretable and portable basis for dimension reduction, and a robust analysis of liquidity dynamics using rolling window metrics. For the 5 bps pools, the leading empirical eigenfunctions explain the majority of cross-tick variation and remain stable, aligning closely with a low-order Legendre polynomial basis. This alignment provides a parsimonious and interpretable structure, similar to the dynamic Nelson-Siegel method for yield curves. The factor coefficients exhibit a time series structure well-captured by AR(1) models with clear GARCH-type heteroskedasticity and heavy-tailed innovations.

q-fin.TR↗

arXiv2024

A mathematical framework for modelling CLMM dynamics in continuous time

This paper develops a rigorous mathematical framework for analyzing Concentrated Liquidity Market Makers (CLMMs) in Decentralized Finance (DeFi) within a continuous-time setting. We model the evolution of liquidity profiles as measure-valued processes and characterize their dynamics under continuous trading. Our analysis encompasses two critical aspects of CLMMs: the mechanics of concentrated liquidity provision and the strategic behavior of arbitrageurs. We examine three distinct arbitrage models -- myopic, finite-horizon, and infinite-horizon with discounted and ergodic controls -- and derive closed-form solutions for optimal arbitrage strategies under each scenario. Importantly, we demonstrate that the presence of trading fees fundamentally constrains the admissible price processes, as the inclusion of fees precludes the existence of diffusion terms in the price process to avoid infinite fee generation. This finding has significant implications for CLMM design and market efficiency.

q-fin.MF↗

arXiv2024

Stylized facts in Web3

This paper presents a comprehensive statistical analysis of the Web3 ecosystem, comparing various Web3 tokens with traditional financial assets across multiple time scales. We examine probability distributions, tail behaviors, and other key stylized facts of the returns for a diverse range of tokens, including decentralized exchanges, liquidity pools, and centralized exchanges. Despite functional differences, most tokens exhibit well-established empirical facts, including unconditional probability density of returns with heavy tails gradually becoming Gaussian and volatility clustering. Furthermore, we compare assets traded on centralized (CEX) and decentralized (DEX) exchanges, finding that DEXs exhibit similar stylized facts despite different trading mechanisms and often divergent long-term performance. We propose that this similarity is attributable to arbitrageurs striving to maintain similar centralized and decentralized prices. Our study contributes to a better understanding of the dynamics of Web3 tokens and the relationship between CEX and DEX markets, with important implications for risk management, pricing models, and portfolio construction in the rapidly evolving DeFi landscape. These results add to the growing body of literature on cryptocurrency markets and provide insights that can guide the development of more accurate models for DeFi markets.

q-fin.ST↗

arXiv2024

An arbitrage driven price dynamics of Automated Market Makers in the presence of fees

We present a model for price dynamics in the Automated Market Makers (AMM) setting. Within this framework, we propose a reference market price following a geometric Brownian motion. The AMM price is constrained by upper and lower bounds, determined by constant multiplications of the reference price. Through the utilization of local times and excursion-theoretic approaches, we derive several analytical results, including its time-changed representation and limiting behavior.

q-fin.MF↗

arXiv2021

Finiteness properties of the category of mod $p$ representations of $\mathrm{GL}_2(\mathbb{Q}_p)$

We establish Bernstein-centre type of results for the category of mod $p$ representations of $\mathrm{GL}_2(\mathbb{Q}_p)$. We treat all the remaining open cases, which occur when $p$ is $2$ or $3$. Our arguments carry over for all primes $p$. This allows us to remove the restrictions on the residual representation at $p$ in Lue Pan's recent proof of the Fontaine--Mazur conjecture for Hodge--Tate representations of $\mathrm{Gal}(\overline{\mathbb Q}/\mathbb{Q})$ with equal Hodge--Tate weights.

math.RT↗

arXiv2021

On the automorphy of 2-dimensional potentially semi-stable deformation rings of $G_{\mathbb{Q}_p}$

Using $p$-adic local Langlands correspondence for $\operatorname{GL}_2(\mathbb{Q}_p)$, we prove that the support of patched modules constructed by Caraiani, Emerton, Gee, Geraghty, Paskunas, and Shin meet every irreducible component of the potentially semistable deformation ring. This gives a new proof of the Breuil-Mézard conjecture for 2-dimensional representations of the absolute Galois group of $\mathbb{Q}_p$ when $p > 2$, which is new in the case $p = 3$ and $\bar{r}$ a twist of an extension of the trivial character by the mod p cyclotomic character. As a consequence, a local restriction in the proof of Fontaine-Mazur conjecture by Kisin is removed.

math.NT↗

arXiv2021

On the modularity of 2-adic potentially semi-stable deformation rings

Using $p$-adic local Langlands correspondence for $\operatorname{GL}_2(\mathbb{Q}_2)$ and an ordinary $R = \mathbb{T}$ theorem, we prove that the support of patched modules for quaternionic forms meet every irreducible component of the potentially semi-stable deformation ring. This gives a new proof of the Breuil-Mézard conjecture for 2-dimensional representations of the absolute Galois group of $\mathbb{Q}_2$, which is new in the case $\overline{r}$ a twist of an extension of the trivial character by itself. As a consequence, a local restriction in Paškūnas' proof of Fontaine-Mazur conjecture is removed.

math.NT↗