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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. 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.
    • 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 Aug 2023.
    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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