Before revision:  We provide here a comprehensive mathematical formulation of the model and show using martingale arguments in the spirit of Sannikov \mbox{%DIFAUXCMD san how the maximization problem with implicit constraints faced by investors can be reduced to a classic stochastic control problem.
After revision:  We provide here a comprehensive mathematical formulation of the model and show using martingale arguments in the spirit of Sannikov \mbox{%DIFAUXCMD san how the maximization problem with implicit constraints faced by investors can be reduced to a classical stochastic control problem.