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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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    Keywords

    Decentralized finance; Automated market makers; Arbitrage; Impermanent loss; Divergence loss;
    All these keywords.

    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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