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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.

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  • Nicole Tianjiao Yang & Tomoyuki Ichiba, 2023. "Relative Arbitrage Opportunities in an Extended Mean Field System," Papers 2311.02690, arXiv.org.
    • 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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