  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.
