We assume that the wealth process X' is self-financing and generated from the initial wealth by holding a fraction u of Xu in a risky stock (whose price follows a geometric Brownian motion) and the remaining fraction 1 u of Xu in a riskless bond (whose price compounds exponentially with interest rate r E R). Letting Pt,x denote a probability measure under which Xu takes value x at time t, we study the dynamic version of the nonlinear optimal control problem info Var (X1-,) where the infimum is taken over admissible controls u subject to Xt > e '(T t)g and Et,xT > /3 for t E [0,. The two constants g and /3 are assumed to be given exogenously and fixed. By conditioning on the expected terminal wealth value, we show that the nonlinear problem can be reduced to a family of linear problems. Solving the latter using a martingale method combined with Lagrange multipliers, we derive the dynamically optimal control ul in closed form and prove that the dynamically optimal terminal wealth XI can only take two values g and /3. This binomial nature of the dynamically optimal strategy stands in sharp contrast with other known portfolio selection strategies encountered in the literature. A direct comparison shows that the dynamically optimal (time-consistent) strategy outperforms the statically optimal (time-inconsistent) strategy in the problem.