Liquidity provision of utility indifference type in decentralized exchanges

Fukasawa, Masaaki; Maire, Basile; Wunsch, Marcus

Digital Finance, 2025, 7, 255-273

Number of Access:64（2025-08-14 02:27 Counts）

Identifier to cite or link to this item: https://hdl.handle.net/11094/101963

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Title
Liquidity provision of utility indifference type in decentralized exchanges
Creator
NRID
1000070506451 1000070506451
ORCID
0000-0002-0848-5001 0000-0002-0848-5001
researchmap permalink
read0140655 read0140655
Scopus Author ID
24366273400 24366273400
CreatorName
Fukasawa, Masaaki
CreatorName
Maire, Basile
CreatorName
Wunsch, Marcus
Subject
Decentralized finance
Automated market makers
Arbitrage
Impermanent loss
Divergence loss
Description
This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s42521-025-00128-5
Abstract
We present a mathematical formulation of liquidity provision in decentralized exchanges. We focus on constant function market makers of utility indifference type, which include constant product market makers with concentrated liquidity as a special case. First, we examine no-arbitrage conditions for a liquidity pool and compute an optimal arbitrage strategy when there is an external liquid market. Second, we show that liquidity provision suffers from impermanent loss unless a transaction fee is levied under the general framework with concentrated liquidity. Third, we establish the well-definedness of arbitrage-free reserve processes of a liquidity pool in continuous-time and show that there is no loss-versus-rebalancing under a nonzero fee if the external market price is continuous. We then argue that liquidity provision by multiple liquidity providers can be understood as liquidity provision by a representative liquidity provider, meaning that the analysis boils down to that for a single liquidity provider. Last, but not least, we give an answer to the fundamental question in which sense the very construction of constant function market makers with concentrated liquidity in the popular platform Uniswap v3 is optimal.
Publisher
Springer International Publishing
Source Title
Digital Finance
Volume (Issue)
7
Page
255-273
Date of Issued
2025-05-09
Language
English
Handle URL
https://hdl.handle.net/11094/101963
PISSN
25246984
eISSN
25246186
Relation.isVersionOf
DOI (Publisher Version)
https://doi.org/10.1007/s42521-025-00128-5
Access Rights
embargoed access
CopyRight
© The Authors, under exclusive licence to Springer Nature Switzerland AG 2025.
The full-text file will be made open to the public on 9 May 2026 in accordance with the publisher's policy.
oaire:version
Accepted Manuscript
Category
学術雑誌論文 Journal Article