Asymptotic analysis for optimal investment and consumption with transaction costs

We consider an agent who invests in a stock and a money market and consumes in order to maximize the utility of consumption over an infinite planning horizon in the presence of a proportional transaction cost lambda > 0. The utility function is of the form U(c) = c(1-p)/(l - p) for p > 0, p not approximate to 1. We provide a heuristic and a rigorous derivation of the asymptotic expansion of the value function in powers of lambda(1/3), and we also obtain asymptotic results on the boundary of the "no-trade" region.