IDEAS home Printed from https://ideas.repec.org/h/wsi/wschap/9789812799579_0022.html
   My bibliography  Save this book chapter

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
    as

    Download full text from publisher

    File URL: https://www.worldscientific.com/doi/pdf/10.1142/9789812799579_0022
    Download Restriction: Ebook Access is available upon purchase.
    File URL: https://www.worldscientific.com/doi/abs/10.1142/9789812799579_0022
    Download Restriction: Ebook Access is available upon purchase.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    4. 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.
    5. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
    6. I. Bajeux-Besnainou & R. Portait, 1997. "The numeraire portfolio: a new perspective on financial theory," The European Journal of Finance, Taylor & Francis Journals, vol. 3(4), pages 291-309.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 1-22, March.
    2. Hans Buhlmann & Eckhard Platen, 2002. "A Discrete Time Benchmark Approach for Finance and Insurance," Research Paper Series 74, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Kevin Fergusson & Eckhard Platen, 2017. "Less-Expensive Valuation of Long Term Annuities Linked to Mortality, Cash and Equity," Papers 1711.02808, arXiv.org.
    5. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 19, July-Dece.
    6. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2009.
    7. Eckhard Platen, 2011. "A Benchmark Approach to Investing and Pricing," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 28, pages 409-426, World Scientific Publishing Co. Pte. Ltd..
    8. repec:dau:papers:123456789/5374 is not listed on IDEAS
    9. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    10. Eckhard Platen, 2005. "On The Role Of The Growth Optimal Portfolio In Finance," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 365-388, December.
    11. Nicola Bruti-Liberati & Christina Nikitopoulos-Sklibosios & Eckhard Platen, 2010. "Real-world jump-diffusion term structure models," Quantitative Finance, Taylor & Francis Journals, vol. 10(1), pages 23-37.
    12. Kevin Fergusson & Eckhard Platen, 2013. "Real World Pricing of Long Term Cash-Linked Annuities and Equity-Linked Annuities with Cash-Linked Guarantees," Research Paper Series 338, Quantitative Finance Research Centre, University of Technology, Sydney.
    13. Keith A. Lewis, 2019. "A Simple Proof of the Fundamental Theorem of Asset Pricing," Papers 1912.01091, arXiv.org.
    14. Eckhard Platen, 2004. "Capital Asset Pricing for Markets with Intensity Based Jumps," Research Paper Series 143, Quantitative Finance Research Centre, University of Technology, Sydney.
    15. Nguyen, Pascal & Portait, Roland, 2002. "Dynamic asset allocation with mean variance preferences and a solvency constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 26(1), pages 11-32, January.
    16. Eckhard Platen, 2003. "Pricing and Hedging for Incomplete Jump Diffusion Benchmark Models," Research Paper Series 110, Quantitative Finance Research Centre, University of Technology, Sydney.
    17. repec:uts:finphd:40 is not listed on IDEAS
    18. A Craig Burnside & Jeremy J Graveline, 2020. "On the Asset Market View of Exchange Rates," The Review of Financial Studies, Society for Financial Studies, vol. 33(1), pages 239-260.
    19. Dong‐Hyun Ahn & H. Henry Cao & Stéphane Chrétien, 2009. "Portfolio Performance Measurement: a No Arbitrage Bounds Approach," European Financial Management, European Financial Management Association, vol. 15(2), pages 298-339, March.
    20. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    21. Eckhard Platen, 2004. "A Benchmark Framework for Risk Management," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 15, pages 305-335, World Scientific Publishing Co. Pte. Ltd..
    22. Brisset, Nicolas, 2017. "On Performativity: Option Theory And The Resistance Of Financial Phenomena," Journal of the History of Economic Thought, Cambridge University Press, vol. 39(4), pages 549-569, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:wschap:9789812799579_0022. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscientific.com/page/worldscibooks .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.