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The uniform integrability of Martingales. On a question by Alexander Cherny

Ruf, Johannes (2015) The uniform integrability of Martingales. On a question by Alexander Cherny. Stochastic Processes and Their Applications, 125 (10). pp. 3657-3662. ISSN 0304-4149

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Identification Number: 10.1016/j.spa.2015.04.002

Abstract

Let X be a progressively measurable, almost surely right-continuous stochastic process such that Xτ ∈ L 1 and E[Xτ ] = E[X0] for each finite stopping time τ . In 2006, Cherny showed that X is then a uniformly integrable martingale provided that X is additionally nonnegative. Cherny then posed the question whether this implication also holds even if X is not necessarily nonnegative. We provide an example that illustrates that this implication is wrong, in general. If, however, an additional integrability assumption is made on the limit inferior of |X| then the implication holds. Finally, we argue that this

Item Type: Article
Official URL: https://www.journals.elsevier.com/stochastic-proce...
Additional Information: © 2015 Elsevier
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 11 Oct 2017 11:13
Last Modified: 20 Mar 2019 02:48
URI: http://eprints.lse.ac.uk/id/eprint/84584

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