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Projective system approach to the martingale characterization of the absence of arbitrage

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  • Balbás, Alejandro
  • Mirás, Miguel Ángel
  • Muñoz-Bouzo, María José

Abstract

The equivalence between the absence of arbitrage and the existence of an equivalent martingale measure fails when an infinite number of trading dates is considered. By enlarging the set of states of nature and the probability measure through a projective system of topological spaces and Radon measures, we characterize the absence of arbitrage when the time set is countable.

Suggested Citation

  • Balbás, Alejandro & Mirás, Miguel Ángel & Muñoz-Bouzo, María José, 2001. "Projective system approach to the martingale characterization of the absence of arbitrage," DEE - Working Papers. Business Economics. WB wb011505, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    • Handle: RePEc:cte:wbrepe:wb011505
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    References listed on IDEAS

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    1. W. Schachermayer, 1994. "Martingale Measures For Discrete‐Time Processes With Infinite Horizon," Mathematical Finance, Wiley Blackwell, vol. 4(1), pages 25-55, January.
    2. 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.
    3. 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.
    4. 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.
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