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Recursive robust estimation and control without commitment

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  • Hansen, Lars Peter
  • Sargent, Thomas J.

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 136 (2007)
Issue (Month): 1 (September)
Pages: 1-27

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Handle: RePEc:eee:jetheo:v:136:y:2007:i:1:p:1-27

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Web page: http://www.elsevier.com/locate/inca/622869

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  1. John Y. Campbell & Jens Hilscher & Jan Szilagyi, 2006. "In Search of Distress Risk," NBER Working Papers 12362, National Bureau of Economic Research, Inc.
  2. Falko Fecht & Kevin Huang, 2004. "Financial intermediaries, markets, and growth," Econometric Society 2004 North American Summer Meetings 419, Econometric Society.
  3. Koetter, M. & Bos, J.W.B. & Heid, F. & Kolari, J.W. & Kool, C.J.M. & Porath, D., 2007. "Accounting for distress in bank mergers," Journal of Banking & Finance, Elsevier, vol. 31(10), pages 3200-3217, October.
  4. 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.
  5. Jovanovic, Boyan, 1982. "Selection and the Evolution of Industry," Econometrica, Econometric Society, vol. 50(3), pages 649-70, May.
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