Abstract
The current economic and financial context should be a confirmation, after also decades of research on asset pricing, of the importance of modeling asset dynamics with processes including jumps, or even pure jump processes. This article exposes in a self-contained framework how portfolio optimization can be conducted when asset returns are modeled by general combinations of Brownian motions and pure-jump L´evy processes. This article also shows how the weights and consumption obtained in the continuous framework of Merton [1969, 1971] and in the jump-diffusion contribution of A¨ıt-Sahalia, Cacho-Diaz and Hurd [2009] can be recovered.