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Local martingales and the fundamental asset pricing theorems in the discrete-time case

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Abstract.

This paper is devoted to giving simpler proofs of the two fundamental theorems of asset pricing theory, in iscrete-time and finite horizon: namely the no-arbitrage theorem, and the market completeness theorem. Some elementary but apparently new results are also given on discrete-time martingale theory, and in particular a new condition for a local martingale to be a martingale.

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Authors and Affiliations

  1. Laboratoire de Probabilités, Université P. et M. Curie et CNRS, URA 224, 4 Place Jussieu, F-75252-Paris Cedex, France , , , , , , FR

    J. Jacod

  2. Steklov Mathematical Institute, Gubkina St. 8, Moscow, 117966 Russia , , , , , , RU

    A.N. Shiryaev

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  1. J. Jacod
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  2. A.N. Shiryaev
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Manuscript received: October 1996; final version received: December 1997

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Jacod, J., Shiryaev, A. Local martingales and the fundamental asset pricing theorems in the discrete-time case. Finance Stochast 2, 259–273 (1998). https://doi.org/10.1007/s007800050040

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  • DOI: https://doi.org/10.1007/s007800050040

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