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Aggregation of financial markets

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  • Georg Menz
  • Moritz Vo{ss}

Abstract

We present a formal framework for the aggregation of financial markets mediated by arbitrage. Our main tool is to characterize markets via utility functions and to employ a one-to-one correspondence to limit order book states. Inspired by the theory of thermodynamics, we argue that the arbitrage-mediated aggregation mechanism gives rise to a market-dynamical entropy, which quantifies the loss of liquidity caused by aggregation. As a concrete guiding example, we illustrate our general approach with the Uniswap v2 automated market maker protocol used in decentralized cryptocurrency exchanges, which we characterize as a so-called ideal market. We derive its equivalent limit order book representation and explicitly compute the arbitrage-mediated aggregation of two liquidity pools of the same asset pair with different marginal prices. We also discuss future directions of research in this emerging theory of market dynamics.

Suggested Citation

  • Georg Menz & Moritz Vo{ss}, 2023. "Aggregation of financial markets," Papers 2309.04116, arXiv.org, revised Sep 2024.
    • Handle: RePEc:arx:papers:2309.04116
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    References listed on IDEAS

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    1. Paul Embrechts & Marius Hofert, 2013. "A note on generalized inverses," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 423-432, June.
    2. Maxim Bichuch & Zachary Feinstein, 2022. "Axioms for Automated Market Makers: A Mathematical Framework in FinTech and Decentralized Finance," Papers 2210.01227, arXiv.org, revised Feb 2025.
    3. Deborah Miori & Mihai Cucuringu, 2022. "DeFi: data-driven characterisation of Uniswap v3 ecosystem & an ideal crypto law for liquidity pools," Papers 2301.13009, arXiv.org, revised Jan 2023.
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