Tootfinder

Optimal Decisions for Liquid Staking: Allocation and Exit Timing
Ruofei Ma, Zhebiao Cai, Wenpin Tang, David Yao
https://arxiv.org/abs/2507.14810 https://ar…

Optimal Decisions for Liquid Staking: Allocation and Exit Timing
In this paper, we study an investor's optimal entry and exit decisions in a liquid staking protocol (LSP) and an automated market maker (AMM), primarily from the standpoint of the investor. Our analysis focuses on two key investor actions: the initial allocation decision at time t=0, and the optimal timing of exit. First, we derive an optimal allocation strategy that enables the investor to distribute risk across the LSP, AMM, and direct holding. Our results also offer insights for LSP and AMM …

Optimal Exit Time for Liquidity Providers in Automated Market Makers
Philippe Bergault, S\'ebastien Bieber, Leandro S\'anchez-Betancourt
https://arxiv.org/abs/2509.06510

Optimal Exit Time for Liquidity Providers in Automated Market Makers
We study the problem of optimal liquidity withdrawal for a representative liquidity provider (LP) in an automated market maker (AMM). LPs earn fees from trading activity but are exposed to impermanent loss (IL) due to price fluctuations. While existing work has focused on static provision and exogenous exit strategies, we characterise the optimal exit time as the solution to a stochastic control problem with an endogenous stopping time. Mathematically, the LP's value function is shown to satisf…

Dynamic Exponent Market Maker: Personalized Portfolio Manager and One Pool to Trade Them All
Wittawat Kositwattanarerk
https://arxiv.org/abs/2507.22732 https://

Dynamic Exponent Market Maker: Personalized Portfolio Manager and One Pool to Trade Them All
Decentralized exchange platforms such as Uniswap and Balancer operate on several pools where each pool contains two or more cryptocurrencies and constitutes direct trading pairs. The drawbacks here are that liquidity providing requires contribution of tokens in a specific proportion, and trading may require hopping between pools, hence increasing transaction fee and gas fee. We propose an automated market maker (AMM) protocol where liquidity providers can deposit any amount of tokens into the p…

EnerSwap: Large-Scale, Privacy-First Automated Market Maker for V2G Energy Trading
Ahmed Mounsf Rafik Bendada, Yacine Ghamri-Doudane
https://arxiv.org/abs/2508.18942 https://

EnerSwap: Large-Scale, Privacy-First Automated Market Maker for V2G Energy Trading
With the rapid growth of Electric Vehicle (EV) technology, EVs are destined to shape the future of transportation. The large number of EVs facilitates the development of the emerging vehicle-to-grid (V2G) technology, which realizes bidirectional energy exchanges between EVs and the power grid. This has led to the setting up of electricity markets that are usually confined to a small geographical location, often with a small number of participants. Usually, these markets are manipulated by inter…

Modeling Loss-Versus-Rebalancing in Automated Market Makers via Continuous-Installment Options
Srisht Fateh Singh, Reina Ke Xin Li, Samuel Gaskin, Yuntao Wu, Jeffrey Klinck, Panagiotis Michalopoulos, Zissis Poulos, Andreas Veneris
https://arxiv.org/abs/2508.02971

Modeling Loss-Versus-Rebalancing in Automated Market Makers via Continuous-Installment Options
This paper mathematically models a constant-function automated market maker (CFAMM) position as a portfolio of exotic options, known as perpetual American continuous-installment (CI) options. This model replicates an AMM position's delta at each point in time over an infinite time horizon, thus taking into account the perpetual nature and optionality to withdraw of liquidity provision. This framework yields two key theoretical results: (a) It proves that the AMM's adverse-selection cost, loss-v…

Dynamics of Liquidity Surfaces in Uniswap v3
Jimmy Risk, Shen-Ning Tung, Tai-Ho Wang
https://arxiv.org/abs/2509.05013 https://arxiv.org/pdf/2509.05013

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 o…