Perturbative Solutions of Hamilton Jacobi Bellman Equations in Robust Decision Making

28 Pages Posted: 26 May 2002

See all articles by Paolo Vanini

Paolo Vanini

University of Basel

Fabio Trojani

Swiss Finance Institute; University of Geneva

Date Written: April 2002

Abstract

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

Vanini, Paolo and Trojani, Fabio, Perturbative Solutions of Hamilton Jacobi Bellman Equations in Robust Decision Making (April 2002). Available at SSRN: https://ssrn.com/abstract=311821 or http://dx.doi.org/10.2139/ssrn.311821

Paolo Vanini

University of Basel ( email )

Petersplatz 1
Basel, CH-4003
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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