IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v186y2020i1d10.1007_s10957-020-01699-6.html
   My bibliography  Save this article

Risk-Neutral Pricing for Arbitrage Pricing Theory

Author

Listed:
  • Laurence Carassus

    (Léonard de Vinci Pôle Universitaire, Research Center
    Université de Reims-Champagne Ardenne)

  • Miklós Rásonyi

    (Alfréd Rényi Institute of Mathematics)

Abstract

We consider infinite-dimensional optimization problems motivated by the financial model called Arbitrage Pricing Theory. Using probabilistic and functional analytic tools, we provide a dual characterization of the superreplication cost. Then, we show the existence of optimal strategies for investors maximizing their expected utility and the convergence of their reservation prices to the super-replication cost as their risk-aversion tends to infinity.

Suggested Citation

  • Laurence Carassus & Miklós Rásonyi, 2020. "Risk-Neutral Pricing for Arbitrage Pricing Theory," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 248-263, July.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:1:d:10.1007_s10957-020-01699-6
    DOI: 10.1007/s10957-020-01699-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-020-01699-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-020-01699-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. 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. Laurence Carassus & Miklós Rásonyi, 2006. "Convergence of Utility Indifference Prices to the Superreplication Price," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 145-154, August.
    3. Y.M. Kabanov & D.O. Kramkov, 1998. "Asymptotic arbitrage in large financial markets," Finance and Stochastics, Springer, vol. 2(2), pages 143-172.
    4. Brown, Stephen J & Weinstein, Mark I, 1983. "A New Approach to Testing Asset Pricing Models: The Bilinear Paradigm," Journal of Finance, American Finance Association, vol. 38(3), pages 711-743, June.
    5. Khan, M. Ali & Sun, Yeneng, 2003. "Exact arbitrage, well-diversified portfolios and asset pricing in large markets," Journal of Economic Theory, Elsevier, vol. 110(2), pages 337-373, June.
    6. Gur Huberman, 2005. "A Simple Approach to Arbitrage Pricing Theory," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 9, pages 289-308, World Scientific Publishing Co. Pte. Ltd..
    7. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    8. Irene Klein, 2000. "A Fundamental Theorem of Asset Pricing for Large Financial Markets," Mathematical Finance, Wiley Blackwell, vol. 10(4), pages 443-458, October.
    9. Bernard Bensaid & Jean‐Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs1," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86, April.
    10. Miklos Rasonyi & Lukasz Stettner, 2005. "On utility maximization in discrete-time financial market models," Papers math/0505243, arXiv.org.
    11. Oleksii Mostovyi, 2018. "Utility Maximization In A Large Market," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 106-118, January.
    12. De Donno, M. & Guasoni, P. & Pratelli, M., 2005. "Super-replication and utility maximization in large financial markets," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 2006-2022, December.
    13. Dybvig, Philip H & Ross, Stephen A, 1985. "Yes, the APT Is Testable," Journal of Finance, American Finance Association, vol. 40(4), pages 1173-1188, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dongdong Hu & Hasanjan Sayit & Svetlozar T. Rachev, 2021. "Moment Matching Method for Pricing Spread Options with Mean-Variance Mixture L\'evy Motions," Papers 2109.02872, arXiv.org, revised Feb 2024.
    2. Nuerxiati Abudurexiti & Kai He & Dongdong Hu & Hasanjan Sayit, 2021. "A note on closed-form spread option valuation under log-normal models," Papers 2109.05431, arXiv.org, revised Feb 2024.

    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. Laurence Carassus & Miklos Rasonyi, 2019. "Risk-neutral pricing for APT," Papers 1904.11252, arXiv.org, revised Oct 2020.
    2. Miklos Rasonyi, 2015. "Maximizing expected utility in the Arbitrage Pricing Model," Papers 1508.07761, arXiv.org, revised Mar 2017.
    3. Miklós Rásonyi, 2016. "On Optimal Strategies For Utility Maximizers In The Arbitrage Pricing Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(07), pages 1-12, November.
    4. Laurence Carassus & Miklos Rasonyi, 2019. "From small markets to big markets," Papers 1907.05593, arXiv.org, revised Oct 2020.
    5. Suat Teker & Oscar Varela, 1998. "A comparative analysis of security pricing using factor, macrovariable and arbitrage pricing models," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 22(2), pages 21-41, June.
    6. Chadwick, Meltem, 2010. "Performance of Bayesian Latent Factor Models in Measuring Pricing Errors," MPRA Paper 79060, University Library of Munich, Germany.
    7. Nawalkha, Sanjay K., 1997. "A multibeta representation theorem for linear asset pricing theories," Journal of Financial Economics, Elsevier, vol. 46(3), pages 357-381, December.
    8. De Donno, M. & Guasoni, P. & Pratelli, M., 2005. "Super-replication and utility maximization in large financial markets," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 2006-2022, December.
    9. Miklós Rásonyi, 2004. "Arbitrage pricing theory and risk-neutral measures," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 27(2), pages 109-123, December.
    10. Michailidis, G., 2009. "Multivariate methods in examining macroeconomic variables effect on Greek stock market returns, 1997-2004," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 9(1).
    11. Khan, M. Ali & Sun, Yeneng, 2001. "Asymptotic Arbitrage and the APT with or without Measure-Theoretic Structures," Journal of Economic Theory, Elsevier, vol. 101(1), pages 222-251, November.
    12. Gabriel Frahm, 0. "Arbitrage Pricing Theory In Ergodic Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-28.
    13. Goyal, Amit & Pérignon, Christophe & Villa, Christophe, 2008. "How common are common return factors across the NYSE and Nasdaq?," Journal of Financial Economics, Elsevier, vol. 90(3), pages 252-271, December.
    14. Moon K. Kim & Chunchi Wu, 1987. "Macro-Economic Factors And Stock Returns," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 10(2), pages 87-98, June.
    15. Khan, M. Ali & Sun, Yeneng, 2003. "Exact arbitrage, well-diversified portfolios and asset pricing in large markets," Journal of Economic Theory, Elsevier, vol. 110(2), pages 337-373, June.
    16. Hansen, Lars Peter & Jagannathan, Ravi, 1997. "Assessing Specification Errors in Stochastic Discount Factor Models," Journal of Finance, American Finance Association, vol. 52(2), pages 557-590, June.
    17. Steve Satchell, 1999. "The Small Noise Arbitrage Pricing Theory," Research Paper Series 4, Quantitative Finance Research Centre, University of Technology, Sydney.
    18. Ferson, Wayne E. & Sarkissian, Sergei & Simin, Timothy, 1999. "The alpha factor asset pricing model: A parable," Journal of Financial Markets, Elsevier, vol. 2(1), pages 49-68, February.
    19. Jack S. K. Chang & Jean C. H. Loo & Carolyn C. Wu Chang, 1990. "The Pricing Of Futures Contracts And The Arbitrage Pricing Theory," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 13(4), pages 297-306, December.
    20. Rajnish Mehra & Sunil Wahal & Daruo Xie, 2021. "Is idiosyncratic risk conditionally priced?," Quantitative Economics, Econometric Society, vol. 12(2), pages 625-646, May.

    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:spr:joptap:v:186:y:2020:i:1:d:10.1007_s10957-020-01699-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.