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Infinitely many securities and the fundamental theorem of asset pricing

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  • Alejandro Balbas

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  • Anna Downarowicz

    ()

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.

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Bibliographic Info

Paper provided by Universidad Carlos III, Departamento de Economía de la Empresa in its series Business Economics Working Papers with number wb043513.

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Date of creation: Aug 2004
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Handle: RePEc:cte:wbrepe:wb043513

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  1. Elyès Jouini & Hédi Kallal, 1998. "Efficient Trading Strategies in the Presence of Market Frictions," Working Papers 98-31, Centre de Recherche en Economie et Statistique.
  2. repec:fth:inseep:9513 is not listed on IDEAS
  3. 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.
  4. Kallal, Hedi & Jouini, Elyès, 1995. "Martingales and arbitrage in securities markets with transaction costs," Economics Papers from University Paris Dauphine 123456789/5630, Paris Dauphine University.
  5. 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.
  6. Chateauneuf, A. & Kast, R. & Lapied, A., 1992. "Choquet Pricing for Financial Markets with Frictions," G.R.E.Q.A.M., Universite Aix-Marseille III 92a11, Universite Aix-Marseille III.
  7. Kallal, Hedi & Jouini, Elyès, 2001. "Efficient Trading Strategies in the Presence of Market Frictions," Economics Papers from University Paris Dauphine 123456789/4721, Paris Dauphine University.
  8. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(3), pages 203-228.
  9. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
  10. Clark, Stephen A., 1993. "The valuation problem in arbitrage price theory," Journal of Mathematical Economics, Elsevier, vol. 22(5), pages 463-478.
  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. 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.
  13. Walter Schachermayer, 2004. "The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 14(1), pages 19-48.
  14. 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.
  15. 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.
  16. 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.

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