Quadratic BSDEs with jumps: a fixed-point approach
Kazi-Tani, Mohamed Nabil; Possamaï, Dylan; Zhou, Chao (2015), Quadratic BSDEs with jumps: a fixed-point approach, Electronic Journal of Probability, 20, 66. 10.1214/EJP.v20-3363
TypeArticle accepté pour publication ou publié
Journal nameElectronic Journal of Probability
Electronic Journal of Probability and Electronic Communications in Probability
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Abstract (EN)In this article, we prove the existence of bounded solutions of quadratic backward SDEs with jumps, that is to say for which the generator has quadratic growth in the variables (z; u). From a technical point of view, we use a direct fixed point approach as in Tevzadze , which allows us to obtain existence and uniqueness of a solution when the terminal condition is small enough. Then, thanks to a well-chosen splitting, we recover an existence result for general bounded solution. Under additional assumptions, we can obtain stability results and a comparison theorem, which as usual implies uniqueness.
Subjects / KeywordsBSDEs; quadratic growth; jumps; fixed-point theorem
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