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Asymptotic arbitrage in large financial markets

Author

Listed:
  • Y.M. Kabanov

    (Central Economics and Mathematics Institute of the Russian Academy of Sciences, Moscow)

  • D.O. Kramkov

    (Steklov Mathematical Institute of the Russian Academy of Sciences, Gubkina str., 8, 117966 Moscow, Russia)

Abstract

A large financial market is described by a sequence of standard general models of continuous trading. It turns out that the absence of asymptotic arbitrage of the first kind is equivalent to the contiguity of sequence of objective probabilities with respect to the sequence of upper envelopes of equivalent martingale measures, while absence of asymptotic arbitrage of the second kind is equivalent to the contiguity of the sequence of lower envelopes of equivalent martingale measures with respect to the sequence of objective probabilities. We express criteria of contiguity in terms of the Hellinger processes. As examples, we study a large market with asset prices given by linear stochastic equations which may have random volatilities, the Ross Arbitrage Pricing Model, and a discrete-time model with two assets and infinite horizon. The suggested theory can be considered as a natural extension of Arbirage Pricing Theory covering the continuous as well as the discrete time case.

Suggested Citation

  • Y.M. Kabanov & D.O. Kramkov, 1998. "Asymptotic arbitrage in large financial markets," Finance and Stochastics, Springer, vol. 2(2), pages 143-172.
    • Handle: RePEc:spr:finsto:v:2:y:1998:i:2:p:143-172
    Note: received: January 1996; final version received: October 1996
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    More about this item

    Keywords

    Large financial market; continuous trading; asymptotic arbitrage; APM; APT; semimartingale; optional decomposition; contiguity; Hellinger process;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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