Abstract
We extend the valuation of contingent claims in presence of default, collateral and funding to a random functional setting and characterise pre-default value processes by martingales. Pre-default value semimartingales can also be described by BSDEs with random path-dependent coefficients and martingales as drivers. En route, we generalise previous settings by relaxing conditions on the available market informaftion, allowing for an arbitrary default-free filtration and constructing a broad class of default times. Moreover, under stochastic volatility, we characterise pre-default value processes via mild solutions to parabolic semilinear PDEs and give sufficient conditions for mild solutions to exist uniquely and to be classical.
Dokumententyp: | Zeitschriftenartikel |
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Fakultät: | Mathematik, Informatik und Statistik > Mathematik > Finanz- und Versicherungsmathematik |
Themengebiete: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
ISSN: | 1556-5068 |
Sprache: | Englisch |
Dokumenten ID: | 109930 |
Datum der Veröffentlichung auf Open Access LMU: | 19. Mrz. 2024, 07:06 |
Letzte Änderungen: | 19. Mrz. 2024, 07:06 |