Robust control and model misspecification

• 成果类型: Article
• 署名作者: Hansen, Lars Peter; Sargent, Thomas J.; Turmuhambetova, Gauhar; Williams, Noah
• 署名单位: New York University; University of Chicago; Princeton University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2004.12.006
• 发表日期: 2006
• 页码: 45-90
• 关键词: model uncertainty; entropy; Robustness; risk-sensitivity; COMMITMENT; time inconsistency; martingale

摘要

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. (c) 2005 Published by Elsevier Inc.