Asymptotic Analysis for Optimal Investment in Finite Time with Transaction Costs

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.