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Dynamic Arbitrage‐Free Asset Pricing with Proportional Transaction Costs

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  • SHUNMING ZHANG
  • CHUNLEI XU
  • XIAOTIE DENG

Abstract

This paper studies multiperiod asset pricing theory in arbitrage‐free financial markets with proportional transaction costs. The mathematical formulation is based on a Euclidean space for weakly arbitrage‐free security markets and strongly arbitrage‐free security markets. We establish the weakly arbitrage‐free pricing theorem and the strongly arbitrage‐free pricing theorem.

Suggested Citation

  • Shunming Zhang & Chunlei Xu & Xiaotie Deng, 2002. "Dynamic Arbitrage‐Free Asset Pricing with Proportional Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 89-97, January.
    • Handle: RePEc:bla:mathfi:v:12:y:2002:i:1:p:89-97
    DOI: 10.1111/1467-9965.00006
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    1. Xing Jin & Frank Milne, 1999. "The Existence Of Equilibrium In A Financial Market With Transaction Costs," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 14, pages 323-343, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Martin Brown & Tomasz Zastawniak, 2019. "Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs," Papers 1905.01859, arXiv.org, revised May 2019.
    2. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
    3. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    4. Roux, Alet, 2011. "The fundamental theorem of asset pricing in the presence of bid-ask and interest rate spreads," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 159-163, March.
    5. Tomasz Zastawniak, 2024. "Fundamental Theorem of Asset Pricing under fixed and proportional costs in multi-asset setting and finite probability space," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 137-149, June.
    6. Xiaotie Deng & Zhong Li & Shouyang Wang & Hailiang Yang, 2005. "Necessary and Sufficient Conditions for Weak No-Arbitrage in Securities Markets with Frictions," Annals of Operations Research, Springer, vol. 133(1), pages 265-276, January.
    7. Martin Brown & Tomasz Zastawniak, 2020. "Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs," Annals of Finance, Springer, vol. 16(3), pages 423-433, September.
    8. Baccara, Mariagiovanna & Battauz, Anna & Ortu, Fulvio, 2006. "Effective securities in arbitrage-free markets with bid-ask spreads at liquidation: a linear programming characterization," Journal of Economic Dynamics and Control, Elsevier, vol. 30(1), pages 55-79, January.

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