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Recursive robust estimation and control without commitment

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Author Info
Hansen, Lars Peter
Sargent, Thomas J.

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Abstract

In a Markov decision problem with hidden state variables, a posterior distribution serves as a state variable and Bayes' law under an approximating model gives its law of motion. A decision maker expresses fear that his model is misspecified by surrounding it with a set of alternatives that are nearby when measured by their expected log likelihood ratios (entropies). Martingales represent alternative models. A decision maker constructs a sequence of robust decision rules by pretending that a sequence of minimizing players choose increments to a martingale and distortions to the prior over the hidden state. A risk sensitivity operator induces robustness to perturbations of the approximating model conditioned on the hidden state. Another risk sensitivity operator induces robustness to the prior distribution over the hidden state. We use these operators to extend the approach of Hansen and Sargent (1995) to problems that contain hidden states. The worst case martingale is overdetermined, expressing an intertemporal inconsistency of worst case beliefs about the hidden state, but not about observables. --

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Paper provided by Deutsche Bundesbank, Research Centre in its series Discussion Paper Series 1: Economic Studies with number 2005,28.

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Date of creation: 2005
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Handle: RePEc:zbw:bubdp1:4222

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  1. Campbell, John Y. & Hilscher, Jens & Szilagyi, Jan, 2005. "In search of distress risk," Discussion Paper Series 1: Economic Studies 2005,27, Deutsche Bundesbank, Research Centre. [Downloadable!]
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  2. Jovanovic, Boyan, 1982. "Selection and the Evolution of Industry," Econometrica, Econometric Society, vol. 50(3), pages 649-70, May. [Downloadable!] (restricted)
  3. Hamerle, Alfred & Liebig, Thilo & Scheule, Harald, 2004. "Forecasting Credit Portfolio Risk," Discussion Paper Series 2: Banking and Financial Studies 2004,01, Deutsche Bundesbank, Research Centre. [Downloadable!]
  4. Koetter, Michael & Bos, Jaap W. B. & Heid, Frank & Kool, Clemens J. M. & Kolari, James W. & Porath, Daniel, 2005. "Accounting for distress in bank mergers," Discussion Paper Series 2: Banking and Financial Studies 2005,09, Deutsche Bundesbank, Research Centre. [Downloadable!]
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Marco P. Tucci, 2009. "How Robust is Robust Control in the Time Domain?," Department of Economics University of Siena 569, Department of Economics, University of Siena. [Downloadable!]
  2. Raghu Suryanarayanan, 2006. "A Model of Anticipated Regret and Endogenous Beliefs," CSEF Working Papers 161, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy. [Downloadable!]
  3. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2006. "Recursive Smooth Ambiguity Preferences," Carlo Alberto Notebooks 17, Collegio Carlo Alberto, revised 2008. [Downloadable!]
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  4. Raghu Suryanarayanan, 2006. "Implications of Anticipated Regret and Endogenous Beliefs for Equilibrium Asset Prices: A Theoretical Framework," CSEF Working Papers 162, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy. [Downloadable!]
  5. Ju, Nengjiu & Miao, Jianjun, 2009. "Ambiguity, Learning, and Asset Returns," MPRA Paper 14737, University Library of Munich, Germany, revised Apr 2009. [Downloadable!]
  6. Martin Ellison & Thomas J. Sargent, 2009. "A defence of the FOMC," Economics Series Working Papers 457, University of Oxford, Department of Economics. [Downloadable!]
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