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The Second Fundamental Theorem of Asset Pricing: A New Approach

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  • Battig, Robert J
  • Jarrow, Robert A

Abstract

This article presents a new definition of market completeness that is independent of the notions of no arbitrage and equivalent martingale measures. Our definition has many advantages, all shown herein. First, it preserves the Second Fundamental Theorem of Asset Pricing, even in complex economies. Second, under our definition, the market can be complete yet arbitrage opportunities exist. This is important in practice, and stands in contrast to the traditional definitions. Third, under the assumptions of no arbitrage and when used in the standard models, our definition is equivalent to the traditional one. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

Suggested Citation

  • Battig, Robert J & Jarrow, Robert A, 1999. "The Second Fundamental Theorem of Asset Pricing: A New Approach," The Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 1219-1235.
    • Handle: RePEc:oup:rfinst:v:12:y:1999:i:5:p:1219-35
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    Cited by:

    1. Kwamie Dunbar, . "An Empirical Review of United States Corporate Default Swap Valuation: The Implications of Functional Forms," Fordham Economics Dissertations, Fordham University, Department of Economics, number 2005.2.
    2. Tian, Weidong, 2014. "Spanning with indexes," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 111-118.
    3. Kimmel, Robert L., 2004. "Modeling the term structure of interest rates: A new approach," Journal of Financial Economics, Elsevier, vol. 72(1), pages 143-183, April.
    4. Alev{s} v{C}ern'y & Christoph Czichowsky, 2022. "The law of one price in quadratic hedging and mean-variance portfolio selection," Papers 2210.15613, arXiv.org, revised Jan 2024.
    5. Gabriel Frahm, 2013. "Pricing and Valuation under the Real-World Measure," Papers 1304.3824, arXiv.org, revised Jan 2016.
    6. Gabriel Frahm, 2013. "A Modern Approach to the Efficient-Market Hypothesis," Papers 1302.3001, arXiv.org, revised Mar 2014.
    7. Galvani, Valentina & Troitsky, Vladimir G., 2010. "Options and efficiency in spaces of bounded claims," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 616-619, July.
    8. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524, January.
    9. Jaime A. Londo~no, 2003. "State Tameness: A New Approach for Credit Constrains," Papers math/0305274, arXiv.org, revised Feb 2004.
    10. Sanjay K. Nawalkha & Xiaoyang Zhuo, 2020. "A Theory of Equivalent Expectation Measures for Contingent Claim Returns," Papers 2006.15312, arXiv.org, revised May 2022.
    11. Firoozi, Fathali, 2006. "On the martingale property of economic and financial instruments," International Review of Economics & Finance, Elsevier, vol. 15(1), pages 87-96.
    12. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2016. "Universal arbitrage aggregator in discrete-time markets under uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 1-50, January.
    13. Gabriel Frahm, 2016. "Pricing And Valuation Under The Real-World Measure," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-39, February.
    14. Nawalkha, Sanjay K & Zhuo, Xiaoyang, 2020. "A Theory of Equivalent Expectation Measures for Expected Prices of Contingent Claims," OSF Preprints hsxtu, Center for Open Science.
    15. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2016. "Universal arbitrage aggregator in discrete-time markets under uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 1-50, January.
    16. Galvani, Valentina, 2009. "Option spanning with exogenous information structure," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 73-79, January.
    17. Protter, Philip, 2001. "A partial introduction to financial asset pricing theory," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 169-203, February.
    18. Zbigniew Palmowski & {L}ukasz Stettner & Anna Sulima, 2018. "Optimal portfolio selection in an It\^o-Markov additive market," Papers 1806.03496, arXiv.org.
    19. Michael Nwogugu, 2020. "Regret Theory And Asset Pricing Anomalies In Incomplete Markets With Dynamic Un-Aggregated Preferences," Papers 2005.01709, arXiv.org.
    20. Zbigniew Palmowski & Łukasz Stettner & Anna Sulima, 2019. "Optimal Portfolio Selection in an Itô–Markov Additive Market," Risks, MDPI, vol. 7(1), pages 1-32, March.
    21. Galvani, Valentina, 2007. "A note on spanning with options," Mathematical Social Sciences, Elsevier, vol. 54(1), pages 106-114, July.

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