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Infinitely many securities and the fundamental theorem of asset pricing

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  • Balbás, Alejandro
  • Downarowicz, Anna

Abstract

Several authors have pointed out the possible absence of martingale measures for static arbitrage-free markets with an infinite number of available securities. This paper addresses this caveat by drawing on projective systems of probability measures. Firstly, it is shown that there are two distinct sorts of models whose treatment is necessarily different. Secondly, and more important, we analyze those situations for which one can provide a projective system of ó .additive measures whose projective limit may be interpreted as a risk-neutral probability. Hence, the Fundamental Theorem of Asset Pricing is extended so that it can apply for models with infinitely many assets.

Suggested Citation

  • Balbás, Alejandro & Downarowicz, Anna, 2004. "Infinitely many securities and the fundamental theorem of asset pricing," DEE - Working Papers. Business Economics. WB wb043513, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    • Handle: RePEc:cte:wbrepe:wb043513
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    References listed on IDEAS

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    1. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    2. Jouini, Elyes & Kallal, Hedi, 2001. "Efficient Trading Strategies in the Presence of Market Frictions," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 343-369.
    3. A. Chateauneuf & R. Kast & A. Lapied, 1996. "Choquet Pricing For Financial Markets With Frictions1," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 323-330, July.
    4. Back, Kerry & Pliska, Stanley R., 1991. "On the fundamental theorem of asset pricing with an infinite state space," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 1-18.
    5. repec:dau:papers:123456789/5630 is not listed on IDEAS
    6. Clark, Stephen A., 1993. "The valuation problem in arbitrage price theory," Journal of Mathematical Economics, Elsevier, vol. 22(5), pages 463-478.
    7. Chateauneuf, A. & Kast, R. & Lapied, A., 1992. "Choquet Pricing for Financial Markets with Frictions," G.R.E.Q.A.M. 92a11, Universite Aix-Marseille III.
    8. Walter Schachermayer, 2004. "The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 19-48, January.
    9. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    10. J. Jacod & A.N. Shiryaev, 1998. "Local martingales and the fundamental asset pricing theorems in the discrete-time case," Finance and Stochastics, Springer, vol. 2(3), pages 259-273.
    11. Balbas, Alejandro & Miras, Miguel Angel & Munoz-Bouzo, Maria Jose, 2002. "Projective system approach to the martingale characterization of the absence of arbitrage," Journal of Mathematical Economics, Elsevier, vol. 37(4), pages 311-323, July.
    12. repec:crs:wpaper:9513 is not listed on IDEAS
    13. Schachermayer, W., 1992. "A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 249-257, December.
    14. repec:arz:wpaper:eres1993-121 is not listed on IDEAS
    15. 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.
    16. repec:dau:papers:123456789/4721 is not listed on IDEAS
    17. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    18. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    Cited by:

    1. Winslow Strong, 2011. "Fundamental theorems of asset pricing for piecewise semimartingales of stochastic dimension," Papers 1112.5340, arXiv.org.
    2. Winslow Strong, 2014. "Fundamental theorems of asset pricing for piecewise semimartingales of stochastic dimension," Finance and Stochastics, Springer, vol. 18(3), pages 487-514, July.
    3. Miklos Rasonyi, 2015. "Maximizing expected utility in the Arbitrage Pricing Model," Papers 1508.07761, arXiv.org, revised Mar 2017.
    4. Huy N. Chau, 2020. "On robust fundamental theorems of asset pricing in discrete time," Papers 2007.02553, arXiv.org, revised Apr 2024.

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