Supermartingale deflators in the absence of a num\'eraire

Philipp Harms, Chong Liu and Ariel Neufeld

Papers from arXiv.org

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.

Date: 2020-01, Revised 2021-03
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2001.05906

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