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Progressive enlargement of filtrations and Backward SDEs with jumps

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Date
2014
Link to item file
http://hal.archives-ouvertes.fr/hal-00555787
Dewey
Probabilités et mathématiques appliquées
Sujet
exponential utility; decomposition in the reference filtration; progressive enlargement of filtrations; multiple random marked times; quadratic BSDE; Backward SDE
Journal issue
Journal of Theoretical Probability
Volume
27
Number
3
Publication date
2014
Article pages
683-724
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s10959-012-0428-1
URI
https://basepub.dauphine.fr/handle/123456789/9573
Collections
  • CEREMADE : Publications
Metadata
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Author
Lim, Thomas
Kharroubi, Idris
Type
Article accepté pour publication ou publié
Abstract (EN)
This work deals with backward stochastic differential equation (BSDE) with random marked jumps, and their applications to default risk. We show that these BSDEs are linked with Brownian BSDEs through the decomposition of processes with respect to the progressive enlargement of filtrations. We show that the equations have solutions if the associated Brownian BSDEs have solutions. We also provide a uniqueness theorem for BSDEs with jumps by giving a comparison theorem based on the comparison for Brownian BSDEs. We give in particular some results for quadratic BDSEs. As applications, we study the pricing and the hedging of a European option in a complete market with a single jump, and the utility maximization problem in an incomplete market with a finite number of jumps.

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