Related papers: Optimal execution on Uniswap v2/v3 under transient…
Constant product markets with concentrated liquidity (CL) are the most popular type of automated market makers. In this paper, we characterise the continuous-time wealth dynamics of strategic LPs who dynamically adjust their range of…
We introduce a new framework for optimal routing and arbitrage in AMM driven markets. This framework improves on the original best-practice convex optimization by restricting the search to the boundary of the optimal space. We can…
In this paper, we propose a novel solution for the distributed unconstrained optimization problem where the total cost is the summation of time-varying local cost functions of a group networked agents. The objective is to track the optimal…
Automated Market Makers (AMMs) are major centers of matching liquidity supply and demand in Decentralized Finance. Their functioning relies primarily on the presence of liquidity providers (LPs) incentivized to invest their assets into a…
Volume-Weighted Average Price (VWAP) is arguably the most prevalent benchmark for trade execution as it provides an unbiased standard for comparing performance across market participants. However, achieving VWAP is inherently challenging…
Automated Market Makers (AMMs) are essential in Decentralized Finance (DeFi) as they match liquidity supply with demand. They function through liquidity providers (LPs) who deposit assets into liquidity pools. However, the asset trading…
We propose a framework to study the optimal liquidation strategy in a limit order book for large-tick stocks, with spread equal to one tick. All order book events (market orders, limit orders and cancellations) occur according to…
We examine how the introduction of concentrated liquidity has changed the liquidity provision market in automated market makers such as Uniswap. To this end, we compare average liquidity provider returns from trading fees before and after…
Automated market makers (AMMs) are pricing mechanisms utilized by decentralized exchanges (DEX). Traditional AMM approaches are constrained by pricing solely based on their own liquidity pool, without consideration of external markets or…
In this paper, we present a class of nonuniform time-stepping, high-order linear stabilized schemes that can preserve both the discrete energy stability and maximum-bound principle (MBP) for the time-fractional Allen-Cahn equation. To this…
We study optimal trade execution strategies in financial markets with discrete order flow. The agent has a finite liquidation horizon and must minimize price impact given a random number of incoming trade counterparties. Assuming that the…
We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density…
Many physical questions in fluid dynamics can be recast in terms of norm constrained optimisation problems; which in-turn, can be further recast as unconstrained problems on spherical manifolds. Due to the nonlinearities of the governing…
Uplift modeling is a key technique for promotion optimization in recommender systems, but standard methods typically fail to account for interference, where treating one item affects the outcomes of others. This violation of the Stable Unit…
We study portfolio selection in a model with both temporary and transient price impact introduced by Garleanu and Pedersen (2016). In the large-liquidity limit where both frictions are small, we derive explicit formulas for the…
The classical optimal trading problem is the closure of a position in an asset over a time interval; the trader maximizes an expected utility under the constraint that the position be fully closed by terminal time. Since the asset price is…
We study the effect of liquidity freezes on an economic agent optimizing her utility of consumption in a perturbed Black-Scholes-Merton model. The single risky asset follows a geometric Brownian motion but is subject to liquidity shocks,…
We consider a dynamic portfolio optimization problem that incorporates predictable returns, instantaneous transaction costs, price impact, and stochastic volatility, extending the classical results of Garleanu and Pedersen (2013), which…
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…
In this article, we address a class of non convex, integer, non linear mathematical programs using dynamic programming. The mathematical program considered, whose properties are studied in this article, may be used to model the optimal…