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

## 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 |
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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: | 30 Jan 2019 20:08 |

URI: | http://eprints.lse.ac.uk/id/eprint/84584 |

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