Résumé en anglais

We consider a consumption-investment optimization problem for the Kabanov model when the proportional transaction costs rate is constant and the prices are modeled by a Lévy process. We naturally extend the preliminary work of [4] to portfolio processes that are only supposed to be làdlàg. This allows to suitably rebalance portfolio processes which jumps induced by the Lévy process and identify an optimal strategy in the two dimensional case.