General Analytical Solutions for Merton'S-Type Consumption-Investment Problems
University of St.Gallen, Economics Discussion Paper No. 2005-02
45 Pages Posted: 16 Jun 2004
Date Written: January 2005
We solve analytically the Merton's problem of an investor with timeadditive power utility. For general state dynamics, we prove existence of two power series representations of the relevant optimal policies and value functions, which hold for all admissible risk aversion parameters. We characterize all terms in the power series by a recursive formula, allowing analytical computations to arbitrary order. Some applications to explicit model settings highlight a very satisfactory accuracy of nite order approximations provided by our power series solution approach.
Keywords: Hamilton-Jacobi-Bellman equations, Higher Order Asymptotic Policies
JEL Classification: C60, C61, G11
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