Supermartingale deflators in the absence of a num\'eraire
Mathematical Finance
2021-03-18 v3
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.
Cite
@article{arxiv.2001.05906,
title = {Supermartingale deflators in the absence of a num\'eraire},
author = {Philipp Harms and Chong Liu and Ariel Neufeld},
journal= {arXiv preprint arXiv:2001.05906},
year = {2021}
}
Comments
33 pages