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Arbitrage Pricing Systems in a Market Driven by an Itô Process

In: Recent Developments In Mathematical Finance

Author

Listed:
  • Shunlong Luo

    (Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, P. R. China)

  • Jia-an Yan

    (Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, P. R. China)

  • Qiang Zhang

    (Department of Economics and Finance, City University of Hong Kong, Kowloon, Hong Kong, P.R. China)

Abstract

A pair of numeraire and equivalent martingale measure is called an arbitrage pricing system. In a security market driven by an Itô process, if we take the wealth process of an admissible self-financing strategy as a numeraire, then there is a natural family of equivalent martingale measures associated with market prices of risk. A subclass of arbitrage pricing systems is identified explicitly by a maximum entropy rationale in the spirit of Föllmer, Schweizer and Sondermann.

Suggested Citation

  • Shunlong Luo & Jia-an Yan & Qiang Zhang, 2001. "Arbitrage Pricing Systems in a Market Driven by an Itô Process," World Scientific Book Chapters, in: Jiongmin Yong (ed.), Recent Developments In Mathematical Finance, chapter 22, pages 263-271, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812799579_0022
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    References listed on IDEAS

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    1. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187, July.
    2. 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..
    3. Jia-an Yan & Qiang Zhang & Shuguang Zhang, 2000. "Growth Optimal Portfolio in a Market Driven by a Jump-Diffusion-Like Process or a Levy Process," Annals of Economics and Finance, Society for AEF, vol. 1(1), pages 101-116, May.
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    6. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
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