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

Author

Listed:
  • J. Jacod

    (Laboratoire de ProbabilitÊs, UniversitÊ P. et M. Curie et CNRS, URA 224, 4 Place Jussieu, F-75252-Paris Cedex, France)

  • A.N. Shiryaev

    (Steklov Mathematical Institute, Gubkina St. 8, Moscow, 117966 Russia Manuscript)

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.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:finsto:v:2:y:1998:i:3:p:259-273
    Note: received: October 1996; final version received: December 1997
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    More about this item

    Keywords

    Arbitrage; complete models; equivalent martingale measure.;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • D40 - Microeconomics - - Market Structure, Pricing, and Design - - - General

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