  In this paper, we study a class of Quadratic Backward Stochastic Differential
Equations (QBSDE in short) with jumps and unbounded terminal condition. We
extend the class of quadratic semimartingales introduced by Barrieu and El
Karoui (2013) in the jump diffusion model. The properties of these class of
semimartingales lead us to prove existence result for the solution of a
quadratic BSDEs.
