Before revision:  Both the value function and the optimal investment policy for the drawdown problem are given explicitly in terms of their counterparts in the unconstrained problem . Our approach is very general but has an important limitation in that we assume all admissible wealth processes have a continuous running maximum. This allows us to use Azema-Yor processes. The proofs also rely on convergence properties, in the utility function, of the unconstrained problem which are of independent interest .
After revision:  Both the value function and the optimal investment policy for the drawdown problem are given explicitly in terms of their counterparts in the unconstrained problem .