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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
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    References listed on IDEAS

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    1. Irene Klein, 2000. "A Fundamental Theorem of Asset Pricing for Large Financial Markets," Mathematical Finance, Wiley Blackwell, vol. 10(4), pages 443-458, October.
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    3. 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..
    4. Oleksii Mostovyi, 2018. "Utility Maximization In A Large Market," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 106-118, January.
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    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. 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.
    10. 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.
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    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.

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