We study the behaviour at the terminal time 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 ? In other words does the solution have a left limit at time ? 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.
Accepté le :
DOI : 10.1051/ps/2016024
Mots-clés : Backward stochastic differential equations, jumps, general filtration, singularity
@article{PS_2016__20__480_0,
author = {Popier, A.},
title = {Limit behaviour of {BSDE} with jumps and with singular terminal condition},
journal = {ESAIM: Probability and Statistics},
pages = {480--509},
publisher = {EDP-Sciences},
volume = {20},
year = {2016},
doi = {10.1051/ps/2016024},
zbl = {1355.60080},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2016024/}
}
TY - JOUR AU - Popier, A. TI - Limit behaviour of BSDE with jumps and with singular terminal condition JO - ESAIM: Probability and Statistics PY - 2016 SP - 480 EP - 509 VL - 20 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2016024/ DO - 10.1051/ps/2016024 LA - en ID - PS_2016__20__480_0 ER -
Popier, A. Limit behaviour of BSDE with jumps and with singular terminal condition. ESAIM: Probability and Statistics, Tome 20 (2016), pp. 480-509. doi : 10.1051/ps/2016024. http://www.numdam.org/articles/10.1051/ps/2016024/
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