Before revision:  We derive some necessary and sufficient first order conditions for optimality and we characterize the optimal solution of the investment problem in terms of the "base capacity " process, i.e. the unique solution of a Representation Problem \`a la Bank-El Karoui .
After revision:  We derive some necessary and sufficient first order conditions for optimality and we characterize the optimal solution of the investment problem in terms of the base capacity process, i.e. the unique solution of a Representation Problem \`a la Bank-El Karoui .