Higher Order Asymptotic Optimal Policies for Partial Equilibrium Economies

33 Pages Posted: 12 Apr 2004

See all articles by Roberto G. Ferretti

Roberto G. Ferretti

Università della Svizzera italiana - Institute of Finance

Fabio Trojani

Swiss Finance Institute; University of Geneva

Date Written: March 2004

Abstract

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

Suggested Citation

Ferretti, Roberto G. and Trojani, Fabio, Higher Order Asymptotic Optimal Policies for Partial Equilibrium Economies (March 2004). Available at SSRN: https://ssrn.com/abstract=516782 or http://dx.doi.org/10.2139/ssrn.516782

Roberto G. Ferretti

Università della Svizzera italiana - Institute of Finance ( email )

CH-6900 Lugano, TN Ticino 6900
Switzerland

Fabio Trojani (Contact Author)

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

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