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August 2014 Progressive enlargements of filtrations with pseudo-honest times
Libo Li, Marek Rutkowski
Ann. Appl. Probab. 24(4): 1509-1553 (August 2014). DOI: 10.1214/13-AAP955

Abstract

We deal with various alternative decompositions of $\mathbb{F}$-martingales with respect to the filtration $\mathbb{G}$, which represents the enlargement of a filtration $\mathbb{F}$ by a progressive flow of observations of a random time that either belongs to the class of pseudo-honest times or satisfies the extended density hypothesis. Several related results from the existing literature are revisited and essentially extended. Results on $\mathbb{G}$-semimartingale decompositions of $\mathbb{F}$-local martingales are crucial for applications in financial mathematics, most notably in the context of credit risk modeling and the study of insider trading where the enlarged filtration plays a vital role. We outline potential applications of our results to problems arising in financial mathematics.

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Libo Li. Marek Rutkowski. "Progressive enlargements of filtrations with pseudo-honest times." Ann. Appl. Probab. 24 (4) 1509 - 1553, August 2014. https://doi.org/10.1214/13-AAP955

Information

Published: August 2014
First available in Project Euclid: 14 May 2014

zbMATH: 1327.60100
MathSciNet: MR3211003
Digital Object Identifier: 10.1214/13-AAP955

Subjects:
Primary: 60H99
Secondary: 91H99

Keywords: enlarged filtration , pseudo-honest time , random time , semimartingale decomposition

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.24 • No. 4 • August 2014
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