On the Propagation of the Weak Representation Property in Independently Enlarged Filtrations: The General Case
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Contributors
Abstract
In this paper, we investigate the propagation of the weak representation property (WRP) to an independently enlarged filtration. More precisely, we consider an F-semimartingale X possessing the WRP with respect to F and an H-semimartingale Y possessing the WRP with respect to H. Assuming that F and H are independent, we show that the G-semimartingale Z= (X, Y) has the WRP with respect to G, where G: = F∨ H. In our setting, X and Y may have simultaneous jump-times. Furthermore, their jumps may charge the same predictable times. This generalizes all available results about the propagation of the WRP to independently enlarged filtrations.
Details
Original language | English |
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Pages (from-to) | 2194-2216 |
Number of pages | 23 |
Journal | Journal of Theoretical Probability |
Volume | 35 |
Issue number | 4 |
Early online date | 17 Dec 2021 |
Publication status | Published - Dec 2022 |
Peer-reviewed | Yes |
External IDs
Scopus | 85121344066 |
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Keywords
Keywords
- Independent semimartingales, Jacod’s equivalence condition, Progressive enlargement of filtrations, Random measures, Semimartingales, Stochastic integration, Weak representation property