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Existence and uniqueness results for BSDEs with jumps: the whole nine yards

Papapantoleon, Antonis; Possamaï, Dylan; Saplaouras, Alexandros (2018), Existence and uniqueness results for BSDEs with jumps: the whole nine yards, Electronic Journal of Probability, 23, p. 1-68. 10.1214/18-EJP240

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Type
Article accepté pour publication ou publié
Date
2018
Journal name
Electronic Journal of Probability
Volume
23
Publisher
Institute of Mathematical Statistics
Pages
1-68
Publication identifier
Metadata
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Author(s)
Papapantoleon, Antonis
Possamaï, Dylan
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Saplaouras, Alexandros
Abstract (EN)
This paper is devoted to obtaining a wellposedness result for multidimensional BSDEs with possibly unbounded random time horizon and driven by a general martingale in a filtration only assumed to satisfy the usual hypotheses, which in particular may be stochastically discontinuous. We show that for stochastic Lipschitz generators and unbounded, possibly infinite, horizon, these equations admit a unique solution in appropriately weighted spaces. Our result allows in particular to have a wellposedness result for BSDEs driven by discrete approximations of general martingales.
Subjects / Keywords
BSDEs; processes with jumps; stochastically discontinuous martingales; random time horizon; stochastic Lipschitz generator