Electronic Journal of Probability
- Electron. J. Probab.
- Volume 20 (2015), paper no. 66, 28 pp.
Quadratic BSDEs with jumps: a fixed-point approach
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.
Electron. J. Probab., Volume 20 (2015), paper no. 66, 28 pp.
Accepted: 14 June 2015
First available in Project Euclid: 4 June 2016
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Possamai, Dylan; Kazi-Tani, Nabil; Zhou, Chao. Quadratic BSDEs with jumps: a fixed-point approach. Electron. J. Probab. 20 (2015), paper no. 66, 28 pp. doi:10.1214/EJP.v20-3363. https://projecteuclid.org/euclid.ejp/1465067172