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Single Jump Filtrations: Preservation of the Local Martingale Property with Respect to the Filtration Generated by the Local Martingaleстатья
Информация о цитировании статьи получена из
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Дата последнего поиска статьи во внешних источниках: 8 апреля 2022 г.
- Авторы: Gushchin Alexander A., Zhunussova Assylliya K.
- Сборник: Operator Theory and Harmonic Analysis
- Серия: Springer Proceedings in Mathematics & Statistics
- Том: 358
- Год издания: 2021
- Издательство: Springer International Publishing AG
- Местоположение издательства: Cham, Switzerland
- Первая страница: 219
- Последняя страница: 231
- DOI: 10.1007/978-3-030-76829-4_11
- Аннотация: Let M be a local martingale with respect to a so-called single jump filtration ??=??(?,F) generated by a random time ? on a probability space (O,F,P). It was recently mentioned by Herdegen and Herrmann (2016) that M is also a local martingale with respect to the filtration H=??^M that it generates if F is the smallest s-field with respect to which ? is measurable. We provide an example of a local martingale with respect to a general single jump filtration which is not a local martingale with respect to H. Then, we find necessary and sufficient condition for preserving the local martingale property with respect to H. The main idea of our constructions and the proofs is that H is also a single jump filtration generated, in general, by other random time and s-field. Finally, we prove that every s-martingale in considered models is still a s-martingale with respect to the filtration that it generates.
- Добавил в систему: Гущин Александр Александрович