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Chasing Price Drains Liquidity

In: Mathematical Research for Blockchain Economy

Author

Listed:
  • Ruichao Jiang

    (Derivation Technology Ltd.)

  • Long Wen

    (Derivation Technology Ltd.
    The Hong Kong Polytechnic University)

  • Yizhou Cao

    (Derivation Technology Ltd.)

  • Yepeng Ding

    (Hiroshima University)

Abstract

Assuming that the price in a Uniswap v3 style Automated Market Maker (AMM) follows a Geometric Brownian Motion (GBM), we prove that the strategy that adjusts the position of liquidity to track the current price leads to a deterministic and exponentially fast decay of liquidity. Next, assuming that there is a Centralized Exchange (CEX), in which the price follows a GBM and the AMM price mean reverts to the CEX price, we show numerically that the same strategy still leads to decay. Last, we propose a strategy that increases the liquidity even without compounding fees earned through liquidity provision.

Suggested Citation

  • Ruichao Jiang & Long Wen & Yizhou Cao & Yepeng Ding, 2026. "Chasing Price Drains Liquidity," Lecture Notes in Operations Research, in: Stefanos Leonardos & Amir K. Goharshady & William Knottenbelt & Panos Pardalos (ed.), Mathematical Research for Blockchain Economy, pages 304-320, Springer.
    • Handle: RePEc:spr:lnopch:978-3-032-13377-9_15
    DOI: 10.1007/978-3-032-13377-9_15
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