Liquidity provision of utility indifference type in decentralized exchanges

Masaaki Fukasawa (), Basile Maire and Marcus Wunsch
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Masaaki Fukasawa: The University of Osaka
Basile Maire: Quantena AG
Marcus Wunsch: ZHAW School of Management and Law

Digital Finance, 2025, vol. 7, issue 2, No 4, 255-273

Abstract: 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.

Keywords: Decentralized finance; Automated market makers; Arbitrage; Impermanent loss; Divergence loss (search for similar items in EconPapers)
JEL-codes: C02 D47 D53 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s42521-025-00128-5

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