Robustness and ambiguity in continuous time

Lars Peter Hansen; Thomas J. Sargent

doi:10.1016/j.jet.2011.01.004

Robustness and ambiguity in continuous time

Lars Peter Hansen, Thomas J. Sargent

Research output: Contribution to journal › Article › peer-review

Abstract

We use statistical detection theory in a continuous-time environment to provide a new perspective on calibrating a concern about robustness or an aversion to ambiguity. A decision maker repeatedly confronts uncertainty about state transition dynamics and a prior distribution over unobserved states or parameters. Two continuous-time formulations are counterparts of two discrete-time recursive specifications of Hansen and Sargent (2007) [16]. One formulation shares features of the smooth ambiguity model of Klibanoff et al. (2005) and (2009) [24,25]. Here our statistical detection calculations guide how to adjust contributions to entropy coming from hidden states as we take a continuous-time limit.

Original language	English (US)
Pages (from-to)	1195-1223
Number of pages	29
Journal	Journal of Economic Theory
Volume	146
Issue number	3
DOIs	https://doi.org/10.1016/j.jet.2011.01.004
State	Published - May 2011

Keywords

Ambiguity
Entropy
Hidden markov model
Likelihood function
Robustness
Smooth ambiguity
Statistical detection error

ASJC Scopus subject areas

Economics and Econometrics

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10.1016/j.jet.2011.01.004

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@article{c5595e26afa0420b8cd514be78b39f71,

title = "Robustness and ambiguity in continuous time",

abstract = "We use statistical detection theory in a continuous-time environment to provide a new perspective on calibrating a concern about robustness or an aversion to ambiguity. A decision maker repeatedly confronts uncertainty about state transition dynamics and a prior distribution over unobserved states or parameters. Two continuous-time formulations are counterparts of two discrete-time recursive specifications of Hansen and Sargent (2007) [16]. One formulation shares features of the smooth ambiguity model of Klibanoff et al. (2005) and (2009) [24,25]. Here our statistical detection calculations guide how to adjust contributions to entropy coming from hidden states as we take a continuous-time limit.",

keywords = "Ambiguity, Entropy, Hidden markov model, Likelihood function, Robustness, Smooth ambiguity, Statistical detection error",

author = "Hansen, {Lars Peter} and Sargent, {Thomas J.}",

note = "Funding Information: ✩ We thank Anmol Bhandari, Ramon Marimon, Cecilia Parlatore Siritto, an editor, and two referees for very helpful comments on earlier drafts. Lars Peter Hansen{\textquoteright}s contribution was supported in part by the Templeton Foundation. * Corresponding author at: New York University, United States. Fax: +1 212 995 4186. E-mail addresses: [email protected] (L.P. Hansen), [email protected] (T.J. Sargent). Copyright: Copyright 2011 Elsevier B.V., All rights reserved.",

year = "2011",

month = may,

doi = "10.1016/j.jet.2011.01.004",

language = "English (US)",

volume = "146",

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journal = "Journal of Economic Theory",

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AU - Hansen, Lars Peter

AU - Sargent, Thomas J.

N1 - Funding Information: ✩ We thank Anmol Bhandari, Ramon Marimon, Cecilia Parlatore Siritto, an editor, and two referees for very helpful comments on earlier drafts. Lars Peter Hansen’s contribution was supported in part by the Templeton Foundation. * Corresponding author at: New York University, United States. Fax: +1 212 995 4186. E-mail addresses: [email protected] (L.P. Hansen), [email protected] (T.J. Sargent). Copyright: Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011/5

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N2 - We use statistical detection theory in a continuous-time environment to provide a new perspective on calibrating a concern about robustness or an aversion to ambiguity. A decision maker repeatedly confronts uncertainty about state transition dynamics and a prior distribution over unobserved states or parameters. Two continuous-time formulations are counterparts of two discrete-time recursive specifications of Hansen and Sargent (2007) [16]. One formulation shares features of the smooth ambiguity model of Klibanoff et al. (2005) and (2009) [24,25]. Here our statistical detection calculations guide how to adjust contributions to entropy coming from hidden states as we take a continuous-time limit.

AB - We use statistical detection theory in a continuous-time environment to provide a new perspective on calibrating a concern about robustness or an aversion to ambiguity. A decision maker repeatedly confronts uncertainty about state transition dynamics and a prior distribution over unobserved states or parameters. Two continuous-time formulations are counterparts of two discrete-time recursive specifications of Hansen and Sargent (2007) [16]. One formulation shares features of the smooth ambiguity model of Klibanoff et al. (2005) and (2009) [24,25]. Here our statistical detection calculations guide how to adjust contributions to entropy coming from hidden states as we take a continuous-time limit.

KW - Ambiguity

KW - Entropy

KW - Hidden markov model

KW - Likelihood function

KW - Robustness

KW - Smooth ambiguity

KW - Statistical detection error

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JO - Journal of Economic Theory

JF - Journal of Economic Theory

IS - 3

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Robustness and ambiguity in continuous time

Abstract

Keywords

ASJC Scopus subject areas

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