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A Non-equilibrium Geometric No-arbitrage Principle

Author

Listed:
  • Wanxiao Tang

    (Nanjing University of Science and Technology)

  • Peibiao Zhao

    (Nanjing University of Science and Technology)

Abstract

The present paper gets a novel and intimate correspondence between martingale in finances and one-parameter transform group in mathematics. This article confirms a criteria of the no-arbitrage problem in a frictionless financial market and a frictional financial market under the conformal transformation via this correspondence. The geometric no-arbitrage principle posed here also reveals a pricing principle on manifolds.

Suggested Citation

  • Wanxiao Tang & Peibiao Zhao, 2023. "A Non-equilibrium Geometric No-arbitrage Principle," Methodology and Computing in Applied Probability, Springer, vol. 25(3), pages 1-15, September.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:3:d:10.1007_s11009-023-10049-8
    DOI: 10.1007/s11009-023-10049-8
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    References listed on IDEAS

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    1. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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