### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 45-90 |

Number of pages | 46 |

Journal | Journal of Economic Theory |

Volume | 128 |

Issue number | 1 |

DOIs | |

State | Published - May 2006 |

### Fingerprint

### Keywords

- Commitment
- Entropy
- Martingale
- Model uncertainty
- Risk-sensitivity
- Robustness
- Time inconsistency

### ASJC Scopus subject areas

- Economics and Econometrics

### Cite this

*Journal of Economic Theory*,

*128*(1), 45-90. https://doi.org/10.1007/s11149-006-0008-3

**Robust control and model misspecification.** / Hansen, Lars Peter; Sargent, Thomas; Turmuhambetova, Gauhar; Williams, Noah.

Research output: Contribution to journal › Article

*Journal of Economic Theory*, vol. 128, no. 1, pp. 45-90. https://doi.org/10.1007/s11149-006-0008-3

}

TY - JOUR

T1 - Robust control and model misspecification

AU - Hansen, Lars Peter

AU - Sargent, Thomas

AU - Turmuhambetova, Gauhar

AU - Williams, Noah

PY - 2006/5

Y1 - 2006/5

N2 - 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.

AB - 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.

KW - Commitment

KW - Entropy

KW - Martingale

KW - Model uncertainty

KW - Risk-sensitivity

KW - Robustness

KW - Time inconsistency

UR - http://www.scopus.com/inward/record.url?scp=33646385061&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646385061&partnerID=8YFLogxK

U2 - 10.1007/s11149-006-0008-3

DO - 10.1007/s11149-006-0008-3

M3 - Article

AN - SCOPUS:33646385061

VL - 128

SP - 45

EP - 90

JO - Journal of Economic Theory

JF - Journal of Economic Theory

SN - 0022-0531

IS - 1

ER -