Perturbative Solutions of Hamilton Jacobi Bellman Equations in Robust Decision Making
28 Pages Posted: 26 May 2002
Date Written: April 2002
This paper makes use of perturbation theory to solve analytically a class of robust control problems implied by Anderson, Hansen and Sargent (2000) (AHS (2000)) model of a preference for robustness. For the constant opportunity set model, we provide (i) asymptotic expressions that characterize to any order in perturbation theory the implied value function, (ii) closed form expressions for the optimal policies up to second order and (iii) parameter constraints that ensure convergence of the whole perturbation series to a classical solution of the robust Hamilton Jacobi Bellman equation.
Keywords: Hamilton-Jacobi Bellman Equations, Model Misspecification, Perturbation Theory, Robust Decision Making
JEL Classification: C60, C61, G11
Suggested Citation: Suggested Citation