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Risk-Neutral Pricing for Arbitrage Pricing Theory

Author

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  • Laurence Carassus

    (PULV - Pôle Universitaire Léonard de Vinci, LMR - Laboratoire de Mathématiques de Reims - URCA - Université de Reims Champagne-Ardenne - CNRS - Centre National de la Recherche Scientifique)

  • Miklós Rásonyi

    (Alfréd Rényi Institute of Mathematics - MTA - Hungarian Academy of Sciences)

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," Post-Print hal-04842839, HAL.
    • Handle: RePEc:hal:journl:hal-04842839
    DOI: 10.1007/s10957-020-01699-6
    Note: View the original document on HAL open archive server: https://hal.science/hal-04842839v1
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    References listed on IDEAS

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    1. 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.
    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. Irene Klein, 2000. "A Fundamental Theorem of Asset Pricing for Large Financial Markets," Mathematical Finance, Wiley Blackwell, vol. 10(4), pages 443-458, October.
    4. 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.
    5. Oleksii Mostovyi, 2018. "Utility Maximization In A Large Market," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 106-118, January.
    6. Y.M. Kabanov & D.O. Kramkov, 1998. "Asymptotic arbitrage in large financial markets," Finance and Stochastics, Springer, vol. 2(2), pages 143-172.
    7. 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.
    8. 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..
    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. 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.
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    Cited by:

    1. Laurence Carassus & Miklós Rásonyi, 2020. "From small markets to big markets," Post-Print hal-04833471, HAL.

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