Supermartingale deflators in the absence of a num\'eraire

Philipp Harms; Chong Liu; Ariel Neufeld

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arXiv · 2001.05906

Supermartingale deflators in the absence of a num\'eraire

Philipp Harms·Chong Liu·Ariel Neufeld

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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.

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Philipp Harms, Chong Liu, Ariel Neufeld. 2020-01-16. Supermartingale deflators in the absence of a num\'eraire. https://arxiv.org/abs/2001.05906

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