Higher Order Asymptotic Optimal Policies for Partial Equilibrium Economies

We apply perturbation theory to solve the optimal control problem of an investor with time-additive power utility over intermediate consumption and final wealth. Under general conditions we show existence of a power series representation for the prevailing optimal consumption and investment policies around a benchmark model. Each term in the power series is characterized in closed form by a recursive general formula that allows analytical computations up to an (in principle) arbitrary order in perturbation theory