Progressive enlargement of filtrations and Backward SDEs with jumps
Lim, Thomas; Kharroubi, Idris (2014), Progressive enlargement of filtrations and Backward SDEs with jumps, Journal of Theoretical Probability, 27, 3, p. 683-724. http://dx.doi.org/10.1007/s10959-012-0428-1
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00555787
Journal nameJournal of Theoretical Probability
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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.
Subjects / Keywordsexponential utility; decomposition in the reference filtration; progressive enlargement of filtrations; multiple random marked times; quadratic BSDE; Backward SDE
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