Electronic Journal of Probability

Quadratic BSDEs with jumps: a fixed-point approach

Dylan Possamai, Nabil Kazi-Tani, and Chao Zhou

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 66, 28 pp.

Dates
Accepted: 14 June 2015
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067172

Digital Object Identifier
doi:10.1214/EJP.v20-3363

Mathematical Reviews number (MathSciNet)
MR3361254

Zentralblatt MATH identifier
1321.60129

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)

Keywords
BSDEs quadratic growth jumps fixed-point theorem

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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


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