Thumbnail

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

View/Open
Type
Article accepté pour publication ou publié
Date
2015
Journal name
Electronic Journal of Probability
Volume
20
Number
66
Publisher
Electronic Journal of Probability and Electronic Communications in Probability
Publication identifier
Metadata
Show full item record
Author(s)
Kazi-Tani, Mohamed Nabil
Possamaï, Dylan
Zhou, Chao
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 [38], 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 / Keywords
BSDEs; quadratic growth; jumps; fixed-point theorem