Volume 20, 2016
|Page(s)||480 - 509|
|Published online||01 December 2016|
Limit behaviour of BSDE with jumps and with singular terminal condition
LUNAM Université, Université du Maine, Laboratoire Manceau de Mathématiques, Avenue O. Messiaen, 72085 Le Mans cedex 9, France.
Received: 13 January 2016
Revised: 28 September 2016
Accepted: 19 October 2016
We study the behaviour at the terminal time T of the minimal solution of a backward stochastic differential equation when the terminal data can take the value + ∞ with positive probability. In a previous paper [T. Kruse and A. Popier, Stoch. Process. Appl. 126 (2016) 2554–2592], we have proved existence of this minimal solution (in a weak sense) in a quite general setting. But two questions arise in this context and were still open: is the solution right continuous with left limits on [0,T]? In other words does the solution have a left limit at time T? The second question is: is this limit equal to the terminal condition? In this paper, under additional conditions on the generator and the terminal condition, we give a positive answer to these two questions.
Mathematics Subject Classification: 60G99 / 60H99 / 60J15
Key words: Backward stochastic differential equations / jumps / general filtration / singularity
© EDP Sciences, SMAI, 2016
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.