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 in terms of the "base capacity " process, i.e. the unique solution of a Representation Problem \`a la Bank-El Karoui .