Supermartingale deflators in the absence of a numéraire

Philipp Harms; Chong Liu; Ariel Neufeld

doi:10.1007/s11579-021-00299-w

Supermartingale deflators in the absence of a numéraire

Philipp Harms, Chong Liu, Ariel Neufeld^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

In this paper we study arbitrage theory of financial markets in the absence of a numéraire 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 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.

Original language	English
Pages (from-to)	885-915
Number of pages	31
Journal	Mathematics and Financial Economics
Volume	15
Issue number	4
DOIs	https://doi.org/10.1007/s11579-021-00299-w
Publication status	Published - Sept 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

ASJC Scopus Subject Areas

Statistics and Probability
Finance
Statistics, Probability and Uncertainty

Keywords

Absence of a numéraire
Arbitrage of the first kind
Fundamental theorem of asset pricing
NUPBR
Supermartingale deflator

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10.1007/s11579-021-00299-w

Cite this

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AU - Liu, Chong

AU - Neufeld, Ariel

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AB - In this paper we study arbitrage theory of financial markets in the absence of a numéraire 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 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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Supermartingale deflators in the absence of a numéraire

Abstract

Bibliographical note

ASJC Scopus Subject Areas

Keywords

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