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Supermartingale deflators in the absence of a num\'eraire

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  • Philipp Harms
  • Chong Liu
  • Ariel Neufeld

Abstract

In this paper we study arbitrage theory of financial markets in the absence of a num\'eraire both in discrete and continuous time. In our main results, we provide a generalization of the classical equivalence between no unbounded profits with bounded risk (NUPBR) and the existence of a supermartingale deflator. To obtain the desired results, we introduce a new approach based on disintegration of the underlying probability space into spaces where the market crashes at deterministic times.

Suggested Citation

  • Philipp Harms & Chong Liu & Ariel Neufeld, 2020. "Supermartingale deflators in the absence of a num\'eraire," Papers 2001.05906, arXiv.org, revised Mar 2021.
    • Handle: RePEc:arx:papers:2001.05906
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    References listed on IDEAS

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    1. Constantinos Kardaras, 2012. "Market viability via absence of arbitrage of the first kind," Finance and Stochastics, Springer, vol. 16(4), pages 651-667, October.
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