Electronic Journal of Probability

Quadratic BSDEs with jumps: a fixed-point approach

Dylan Possamai, Nabil Kazi-Tani, and Chao Zhou

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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

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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Zentralblatt MATH identifier

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

BSDEs quadratic growth jumps fixed-point theorem

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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

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