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An enlargement of filtration formula with applications to multiple non-ordered default times

Monique Jeanblanc (), Libo Li () and Shiqi Song ()
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Monique Jeanblanc: Université Paris Saclay
Libo Li: University of New South Wales
Shiqi Song: Université Paris Saclay

Finance and Stochastics, 2018, vol. 22, issue 1, 205-240

Abstract: Abstract In this work, for a reference filtration F $\mathbb {F}$ , we develop a method for computing the semimartingale decomposition of F $\mathbb {F}$ -martingales in a specific type of enlargement of F $\mathbb {F}$ . As an application, we study the progressive enlargement of F $\mathbb {F}$ with a sequence of non-ordered default times and show how to deduce results concerning the first-to-default, k $k$ th-to-default, k-out-of-n-to-default or all-to-default events. In particular, using this method, we compute explicitly the semimartingale decomposition of F $\mathbb {F}$ -martingales under the absolute continuity condition of Jacod.

Keywords: Enlargement of filtration; Non-ordered default times; Reduced form credit risk modeling; Semimartingale decomposition; 60G07; 91G40 (search for similar items in EconPapers)
JEL-codes: G14 (search for similar items in EconPapers)
Date: 2018
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