A Note on the Strong Predictable Representation Property and Enlargement of Filtration
The strong predictable representation property of semi-martingales and the notion of enlargement of filtration meet naturally in modeling financial markets, and theoretical problems arise. Here, first, we illustrate some of them through classical examples. Then, we review recent results obtained by...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/10/1783 |
| _version_ | 1827667973205131264 |
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| author | Antonella Calzolari Barbara Torti |
| author_facet | Antonella Calzolari Barbara Torti |
| author_sort | Antonella Calzolari |
| collection | DOAJ |
| description | The strong predictable representation property of semi-martingales and the notion of enlargement of filtration meet naturally in modeling financial markets, and theoretical problems arise. Here, first, we illustrate some of them through classical examples. Then, we review recent results obtained by studying predictable martingale representations for filtrations enlarged by means of a full process, possibly with accessible components in its jump times. The emphasis is on the non-uniqueness of the martingale enjoying the strong predictable representation property with respect to the same enlarged filtration. |
| first_indexed | 2024-03-10T03:27:40Z |
| format | Article |
| id | doaj.art-21602e77173b4be5ad7358f708d1837b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:27:40Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-21602e77173b4be5ad7358f708d1837b2023-11-23T12:02:23ZengMDPI AGMathematics2227-73902022-05-011010178310.3390/math10101783A Note on the Strong Predictable Representation Property and Enlargement of FiltrationAntonella Calzolari0Barbara Torti1Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, I 00133 Roma, ItalyDipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, I 00133 Roma, ItalyThe strong predictable representation property of semi-martingales and the notion of enlargement of filtration meet naturally in modeling financial markets, and theoretical problems arise. Here, first, we illustrate some of them through classical examples. Then, we review recent results obtained by studying predictable martingale representations for filtrations enlarged by means of a full process, possibly with accessible components in its jump times. The emphasis is on the non-uniqueness of the martingale enjoying the strong predictable representation property with respect to the same enlarged filtration.https://www.mdpi.com/2227-7390/10/10/1783predictable representations propertyenlargement of filtrationcompleteness of a financial market |
| spellingShingle | Antonella Calzolari Barbara Torti A Note on the Strong Predictable Representation Property and Enlargement of Filtration Mathematics predictable representations property enlargement of filtration completeness of a financial market |
| title | A Note on the Strong Predictable Representation Property and Enlargement of Filtration |
| title_full | A Note on the Strong Predictable Representation Property and Enlargement of Filtration |
| title_fullStr | A Note on the Strong Predictable Representation Property and Enlargement of Filtration |
| title_full_unstemmed | A Note on the Strong Predictable Representation Property and Enlargement of Filtration |
| title_short | A Note on the Strong Predictable Representation Property and Enlargement of Filtration |
| title_sort | note on the strong predictable representation property and enlargement of filtration |
| topic | predictable representations property enlargement of filtration completeness of a financial market |
| url | https://www.mdpi.com/2227-7390/10/10/1783 |
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