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doi:10.1016/j.jet.2004.12.006    
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Copyright © 2005 Published by Elsevier Inc.

Robust control and model misspecification

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Lars Peter Hansena, Thomas J. Sargentb, Corresponding Author Contact Information, E-mail The Corresponding Author, Gauhar Turmuhambetovac and Noah Williamsc

aDepartment of Economics, University of Chicago, 1126 E. 59th Street, Chicago, Illinois, 60637.

bDepartment of Economics, New York University and Hoover Institution, Stanford, CA. 94305

cDepartment of Economics, Princeton University, Princeton, NJ 08544-1021.


Received 21 April 2004; 
revised 10 December 2004. 
Available online 9 March 2006.

Abstract

A decision maker fears that data are generated by a statistical perturbation of an approximating model that is either a controlled diffusion or a controlled measure over continuous functions of time. A perturbation is constrained in terms of its relative entropy. Several different two-player zero-sum games that yield robust decision rules are related to one another, to the max–min expected utility theory of Gilboa and Schmeidler [Maxmin expected utility with non-unique prior, J. Math. Econ. 18 (1989) 141–153], and to the recursive risk-sensitivity criterion described in discrete time by Hansen and Sargent [Discounted linear exponential quadratic Gaussian control, IEEE Trans. Automat. Control 40 (5) (1995) 968–971]. To represent perturbed models, we use martingales on the probability space associated with the approximating model. Alternative sequential and nonsequential versions of robust control theory imply identical robust decision rules that are dynamically consistent in a useful sense.

Keywords: Model uncertainty; Entropy; Robustness; Risk-sensitivity; Commitment; Time inconsistency; Martingale

JEL classification codes: C61; E61


Corresponding Author Contact InformationCorresponding author.

 
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