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 18 how the maximization problem with implicit constraints faced by investors can be reduced to a classic stochastic control problem.