Volume 56, 2017Enlargement of filtrations
|Page(s)||88 - 110|
|Published online||04 September 2017|
LaMME, University of Evry
2 LaMME, Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise
3 Department of Mathematics, University of Oslo
In this paper, we are interested by advanced backward stochastic differential equations (ABSDEs), in a probability space equipped with a Brownian motion and a single jump process, with a jump at time τ. ABSDEs are BSDEs where the driver depends on the future paths of the solution. We show, that under immersion hypothesis between the Brownian filtration and its progressive enlargement with τ, assuming that the conditional law of τ is equivalent to the unconditional law of τ, and a Lipschitz condition on the driver, the ABSDE has a solution.
This research was supported by Chaire Markets in Transition, (French Banking Federation) Institut Louis Bachelier and Labex ANR 11-LABX-0019.
© EDP Sciences, SMAI 2017
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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