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Liquidity provision of utility indifference type in decentralized exchanges

Author

Listed:
  • Masaaki Fukasawa

    (The University of Osaka)

  • Basile Maire

    (Quantena AG)

  • Marcus Wunsch

    (ZHAW School of Management and Law)

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.

Suggested Citation

  • Masaaki Fukasawa & Basile Maire & Marcus Wunsch, 2025. "Liquidity provision of utility indifference type in decentralized exchanges," Digital Finance, Springer, vol. 7(2), pages 255-273, June.
    • Handle: RePEc:spr:digfin:v:7:y:2025:i:2:d:10.1007_s42521-025-00128-5
    DOI: 10.1007/s42521-025-00128-5
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    References listed on IDEAS

    as
    1. 'Alvaro Cartea & Fayc{c}al Drissi & Marcello Monga, 2023. "Decentralised Finance and Automated Market Making: Predictable Loss and Optimal Liquidity Provision," Papers 2309.08431, arXiv.org, revised Jun 2024.
    2. Vijay Mohan, 2022. "Automated market makers and decentralized exchanges: a DeFi primer," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-48, December.
    3. Joseph Najnudel & Shen-Ning Tung & Kazutoshi Yamazaki & Ju-Yi Yen, 2024. "An arbitrage driven price dynamics of Automated Market Makers in the presence of fees," Papers 2401.01526, arXiv.org.
    4. Barrieu, Pauline & El Karoui, Nicole, 2005. "Inf-convolution of risk measures and optimal risk transfer," LSE Research Online Documents on Economics 2829, London School of Economics and Political Science, LSE Library.
    5. Guillermo Angeris & Alex Evans & Tarun Chitra, 2023. "Replicating market makers," Digital Finance, Springer, vol. 5(2), pages 367-387, June.
    6. Álvaro Cartea & Fayçal Drissi & Marcello Monga, 2023. "Predictable Losses of Liquidity Provision in Constant Function Markets and Concentrated Liquidity Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 30(2), pages 69-93, March.
    7. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, April.
    8. Masaaki Fukasawa & Basile Maire & Marcus Wunsch, 2023. "Weighted variance swaps hedge against impermanent loss," Quantitative Finance, Taylor & Francis Journals, vol. 23(6), pages 901-911, June.
    9. Jason Milionis & Ciamac C. Moallemi & Tim Roughgarden, 2023. "Automated Market Making and Arbitrage Profits in the Presence of Fees," Papers 2305.14604, arXiv.org, revised Jul 2025.
    Full references (including those not matched with items on IDEAS)

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    JEL classification:

    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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