  We consider an agent who invests in a stock and a money market account with
the goal of maximizing the utility of his investment at the final time T in the
presence of a proportional transaction cost. The utility function considered is
power utility. We provide a heuristic and a rigorous derivation of the
asymptotic expansion of the value function in powers of transaction cost
parameter. We also obtain a "nearly optimal" strategy, whose utility
asymptotically matches the leading terms in the value function.
