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

See all articles by Fabio Trojani

Fabio Trojani

Swiss Finance Institute; University of Geneva

Roberto G. Ferretti

Università della Svizzera italiana - Institute of Finance

Date Written: January 2005

Abstract

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

Suggested Citation

Trojani, Fabio and Ferretti, Roberto G., General Analytical Solutions for Merton'S-Type Consumption-Investment Problems (January 2005). University of St.Gallen, Economics Discussion Paper No. 2005-02, Available at SSRN: https://ssrn.com/abstract=556576 or http://dx.doi.org/10.2139/ssrn.556576

Fabio Trojani

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

University of Geneva ( email )

Geneva, Geneva
Switzerland

Roberto G. Ferretti (Contact Author)

Università della Svizzera italiana - Institute of Finance ( email )

CH-6900 Lugano, TN Ticino 6900
Switzerland

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