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Relative Arbitrage Opportunities in an Extended Mean Field System

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  • Nicole Tianjiao Yang
  • Tomoyuki Ichiba

Abstract

This paper studies relative arbitrage opportunities in a market with infinitely many interacting investors. We establish a conditional McKean-Vlasov system to study the market dynamics coupled with investors. We then provide a theoretical framework to study a mean-field system, where the mean-field terms consist of a joint distribution of wealth and strategies. The optimal relative arbitrage is characterized by the equilibrium of extended mean-field games. We show the conditions on the existence and the uniqueness of the mean field equilibrium, then prove the propagation of chaos results for the finite-player game, and demonstrate that the Nash equilibrium converges to the mean field equilibrium when the population grows to infinity.

Suggested Citation

  • Nicole Tianjiao Yang & Tomoyuki Ichiba, 2023. "Relative Arbitrage Opportunities in an Extended Mean Field System," Papers 2311.02690, arXiv.org, revised Oct 2024.
    • Handle: RePEc:arx:papers:2311.02690
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    References listed on IDEAS

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    1. Daniel Fernholz & Ioannis Karatzas, 2010. "On optimal arbitrage," Papers 1010.4987, arXiv.org.
    2. Ting-Kam Wong, 2015. "Optimization of relative arbitrage," Annals of Finance, Springer, vol. 11(3), pages 345-382, November.
    3. Daniel Lacker & Thaleia Zariphopoulou, 2019. "Mean field and n‐agent games for optimal investment under relative performance criteria," Mathematical Finance, Wiley Blackwell, vol. 29(4), pages 1003-1038, October.
    4. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
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