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Geometric No-Arbitrage Analysis in the Dynamic Financial Market with Transaction Costs

Author

Listed:
  • Wanxiao Tang

    (Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China
    These authors contributed equally to this work.)

  • Jun Zhao

    (Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China
    These authors contributed equally to this work.)

  • Peibiao Zhao

    (Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China
    These authors contributed equally to this work.)

Abstract

The present paper considers a class of financial market with transaction costs and constructs a geometric no-arbitrage analysis frame. Then, this paper arrives at the fact that this financial market is of no-arbitrage if and only if the curvature 2-form of a specific connection is zero. Furthermore, this paper derives the fact that the no-arbitrage condition for the one-period financial market is equivalent to the geometric no-arbitrage condition. Finally, an example states the equivalence between the geometric no-arbitrage condition and the existence of the solutions for a maximization problem of expected utility.

Suggested Citation

  • Wanxiao Tang & Jun Zhao & Peibiao Zhao, 2019. "Geometric No-Arbitrage Analysis in the Dynamic Financial Market with Transaction Costs," JRFM, MDPI, vol. 12(1), pages 1-17, February.
    • Handle: RePEc:gam:jjrfmx:v:12:y:2019:i:1:p:26-:d:203891
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    References listed on IDEAS

    as
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