Geodesic
Limit behaviour of BSDE with jumps and with singular terminal condition
Popier, A.1
1 LUNAM Université, Université du Maine, Laboratoire Manceau de Mathématiques, Avenue O. Messiaen, 72085 Le Mans cedex 9, France.
ESAIM: Probability and Statistics, Tome 20 (2016), pp. 480-509

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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.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2016024
Classification : 60G99, 60H99, 60J15
Keywords: Backward stochastic differential equations, jumps, general filtration, singularity

Popier, A. 1

1 LUNAM Université, Université du Maine, Laboratoire Manceau de Mathématiques, Avenue O. Messiaen, 72085 Le Mans cedex 9, France. 
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     title = {Limit behaviour of {BSDE} with jumps and with singular terminal condition},
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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

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