Geodesic
Limit behaviour of BSDE with jumps and with singular terminal condition
Popier, A.1
1LUNAM 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.

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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. 
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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     title = {Limit behaviour of {BSDE} with jumps and with singular terminal condition},
     journal = {ESAIM: Probability and Statistics},
     pages = {480--509},
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