The Annals of Applied Probability

Progressive enlargements of filtrations with pseudo-honest times

Libo Li and Marek Rutkowski

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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.

Article information

Source
Ann. Appl. Probab. Volume 24, Number 4 (2014), 1509-1553.

Dates
First available in Project Euclid: 14 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1400073656

Digital Object Identifier
doi:10.1214/13-AAP955

Mathematical Reviews number (MathSciNet)
MR3211003

Zentralblatt MATH identifier
1327.60100

Subjects
Primary: 60H99: None of the above, but in this section
Secondary: 91H99

Keywords
Random time pseudo-honest time enlarged filtration semimartingale decomposition

Citation

Li, Libo; Rutkowski, Marek. Progressive enlargements of filtrations with pseudo-honest times. Ann. Appl. Probab. 24 (2014), no. 4, 1509--1553. doi:10.1214/13-AAP955. https://projecteuclid.org/euclid.aoap/1400073656


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