We prove the existence of bounded solutions of quadratic backward SDEs with jumps, using a direct fixed-point approach as in Tevzadze (2008). Under an additional standard assumption, we prove a uniqueness result, thanks to a comparison theorem. Then we study the properties of the corresponding g-expectations, we obtain in particular a non-linear Doob-Meyer decomposition for g-submartingales. We also give applications for dynamic risk measures and compute their inf-convolution, with some explicit examples of optimal risk transfer between two agents. This talk is based on joint works with Nabil Kazi-Tani and Dylan Possamai.