Higher Order Asymptotic Optimal Policies for Partial Equilibrium Economies
33 Pages Posted: 12 Apr 2004
Date Written: March 2004
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.
Keywords: Hamilton-Jacobi-Bellman equations, higher order asymptotic policies, Merton model, partial equilibrium, perturbation theory
JEL Classification: C60, C61, G11
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