A QUARTET OF SEMIGROUPS FOR MODEL SPECIFICATION, ROBUSTNESS, PRICES OF RISK, AND MODEL DETECTION

A QUARTET OF SEMIGROUPS FOR MODEL SPECIFICATION, ROBUSTNESS, PRICES OF RISK, AND MODEL DETECTION A representative agent fears that his model, a continuous time Markov process with jump and diffusion components, is misspecified and therefore uses robust control theory to make decisions. Under the decision maker's approximating model, cautious behavior puts adjustments for model misspecification into market prices for risk factors. We use a statistical theory of detection to quantify how much model misspecification the decision maker should fear, given his historical data record. A semigroup is a collection of objects connected by something like the law of iterated expectations. The law of iterated expectations defines the semigroup for a Markov process, while similar laws define other semigroups. Related semigroups describe (1) an approximating model; (2) a model misspecification adjustment to the continuation value in the decision maker's Bellman equation; (3) asset prices; and (4) the behavior of the model detection statistics that we use to calibrate how much robustness the decision maker prefers. Semigroups 2, 3, and 4 establish a tight link between the market price of uncertainty and a bound on the error in statistically discriminating between an approximating and a worst case model. (JEL: C00, D51, D81, E1, G12) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the European Economic Association Oxford University Press

A QUARTET OF SEMIGROUPS FOR MODEL SPECIFICATION, ROBUSTNESS, PRICES OF RISK, AND MODEL DETECTION

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Publisher
Oxford University Press
Copyright
2003 European Economic Association
ISSN
1542-4766
eISSN
1542-4774
DOI
10.1162/154247603322256774
Publisher site
See Article on Publisher Site

Abstract

A representative agent fears that his model, a continuous time Markov process with jump and diffusion components, is misspecified and therefore uses robust control theory to make decisions. Under the decision maker's approximating model, cautious behavior puts adjustments for model misspecification into market prices for risk factors. We use a statistical theory of detection to quantify how much model misspecification the decision maker should fear, given his historical data record. A semigroup is a collection of objects connected by something like the law of iterated expectations. The law of iterated expectations defines the semigroup for a Markov process, while similar laws define other semigroups. Related semigroups describe (1) an approximating model; (2) a model misspecification adjustment to the continuation value in the decision maker's Bellman equation; (3) asset prices; and (4) the behavior of the model detection statistics that we use to calibrate how much robustness the decision maker prefers. Semigroups 2, 3, and 4 establish a tight link between the market price of uncertainty and a bound on the error in statistically discriminating between an approximating and a worst case model. (JEL: C00, D51, D81, E1, G12)

Journal

Journal of the European Economic AssociationOxford University Press

Published: Mar 1, 2003

References

  • Robust Permanent Income and Pricing.
    Hansen, Hansen; Sargent, Sargent; Tallarini, Tallarini

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