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

Joseph  Najnudel; Shen-Ning Tung; Kazutoshi  Yamazaki; Ju-Yi Yen

doi:10.3934/fmf.2024018

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

Joseph Najnudel
, Shen-Ning Tung
, Kazutoshi Yamazaki
, Ju-Yi Yen^*

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

3 Citations (Scopus)

Abstract

Under a reference market price following a geometric Brownian motion, we present a model for price dynamics in the Automated Market Makers (AMM) setting. The AMM price is constrained within bounds determined by constant multiples of this reference price. By employing local time and excursion theory, we derive several analytical results, including a time-changed representation of the AMM price process and its asymptotic behavior.

Original language	English
Pages (from-to)	560-571
Number of pages	12
Journal	Frontiers of Mathematical Finance
Volume	3
Issue number	4
Early online date	1 Nov 2024
DOIs	https://doi.org/10.3934/fmf.2024018
Publication status	Published - 1 Dec 2024

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title = "An arbitrage driven price dynamics of Automated Market Makers in the presence of fees",

abstract = "Under a reference market price following a geometric Brownian motion, we present a model for price dynamics in the Automated Market Makers (AMM) setting. The AMM price is constrained within bounds determined by constant multiples of this reference price. By employing local time and excursion theory, we derive several analytical results, including a time-changed representation of the AMM price process and its asymptotic behavior. ",

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AU - Najnudel, Joseph

AU - Tung, Shen-Ning

AU - Yamazaki, Kazutoshi

AU - Yen, Ju-Yi

PY - 2024/12/1

Y1 - 2024/12/1

N2 - Under a reference market price following a geometric Brownian motion, we present a model for price dynamics in the Automated Market Makers (AMM) setting. The AMM price is constrained within bounds determined by constant multiples of this reference price. By employing local time and excursion theory, we derive several analytical results, including a time-changed representation of the AMM price process and its asymptotic behavior.

AB - Under a reference market price following a geometric Brownian motion, we present a model for price dynamics in the Automated Market Makers (AMM) setting. The AMM price is constrained within bounds determined by constant multiples of this reference price. By employing local time and excursion theory, we derive several analytical results, including a time-changed representation of the AMM price process and its asymptotic behavior.

U2 - 10.3934/fmf.2024018

DO - 10.3934/fmf.2024018

M3 - Article (Academic Journal)

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SP - 560

EP - 571

JO - Frontiers of Mathematical Finance

JF - Frontiers of Mathematical Finance

IS - 4

ER -

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

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