Progressive enlargement of filtrations and Backward SDEs with jumps
type: Dataset
description: 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.
landing page: https://hal.science/hal-00555787
keyword: backward-sde
keyword: decomposition-in-the-reference-filtration
keyword: exponential-utility
keyword: infoeu-reposemanticspreprint
keyword: mathmath-ocmathematics-mathoptimization-and-control-mathoc
keyword: mathmath-prmathematics-mathprobability-mathpr
keyword: msc-classification-2000-60g57-60h20-60j75-91g10-91g80-93e30
keyword: multiple-random-marked-times
keyword: preprints-working-papers-
keyword: progressive-enlargement-of-filtrations
keyword: quadratic-bsde
issued: 2026-05-16T07:00:49.938526
modified: 2026-05-16T07:00:49.938532
language: en
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Progressive enlargement of filtrations and Backward SDEs with jumps
type: Distribution
format: HTML
access URL: https://hal.science/hal-00555787
issued: 2026-05-16T07:00:49.975006
modified: 2026-05-16T07:00:49.910555