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Universal arbitrage aggregator in discrete-time markets under uncertainty

Author

Listed:
  • Matteo Burzoni
  • Marco Frittelli
  • Marco Maggis

Abstract

In a model-independent discrete-time financial market, we discuss the richness of the family of martingale measures in relation to different notions of arbitrage, generated by a class S $\mathcal{S}$ of significant sets, which we call arbitrage de la classe S $\mathcal{S}$ . The choice of S $\mathcal{S}$ reflects the intrinsic properties of the class of polar sets of martingale measures. In particular, for S = { Ω } $\mathcal{S}=\{ \Omega\} $ , absence of model-independent arbitrage is equivalent to the existence of a martingale measure; for S $\mathcal{S}$ being the open sets, absence of open arbitrage is equivalent to the existence of full support martingale measures. These results are obtained by adopting a technical filtration enlargement and by constructing a universal aggregator of all arbitrage opportunities. We further introduce the notion of market feasibility and provide its characterization via arbitrage conditions. We conclude providing a dual representation of open arbitrage in terms of weakly open sets of probability measures, which highlights the robust nature of this concept. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • Matteo Burzoni & Marco Frittelli & Marco Maggis, 2016. "Universal arbitrage aggregator in discrete-time markets under uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 1-50, January.
    • Handle: RePEc:spr:finsto:v:20:y:2016:i:1:p:1-50
    DOI: 10.1007/s00780-015-0283-x
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    References listed on IDEAS

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    More about this item

    Keywords

    Model uncertainty; First fundamental theorem of asset pricing; Feasible market; Open arbitrage; Full support martingale measure; 60G42; 91B24; 91G99; 60H99; 46A20; 46E27; G10; G12; G13;
    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
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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