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Large Financial Markets, Discounting, and No Asymptotic Arbitrage

Author

Listed:
  • Dániel Ágoston Bálint

    (ETH Zurich - Department of Mathematics)

  • Martin Schweizer

    (ETH Zurich; Swiss Finance Institute)

Abstract

For a large financial market (which is a sequence of usual, “small” financial markets), we introduce and study a concept of no asymptotic arbitrage (of the first kind) which is invariant under discounting. We give two dual characterisations of this property in terms of (1) martingale-like properties for each small market plus (2) a contiguity property of suitably chosen “generalised martingale measures” along the sequence of small markets. Our results extend the work of Rokhlin and of Klein/Schachermayer and Kabanov/Kramkov to a discounting-invariant framework. We also show how a market on [0,∞) can be viewed as a large financial market and how no asymptotic arbitrage, both classic and in our new sense, then relates to no-arbitrage properties directly on [0,∞).

Suggested Citation

  • Dániel Ágoston Bálint & Martin Schweizer, 2018. "Large Financial Markets, Discounting, and No Asymptotic Arbitrage," Swiss Finance Institute Research Paper Series 18-70, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1870
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    More about this item

    Keywords

    large financial markets; no asymptotic arbitrage; discounting; NAA; NUPBR; DIWV; ADIWV; tradable deflator;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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