## A Quartet of Semi-Groups for Model Specification, Detection, Robustness, and the Price of Risk

Venue: | Price of Risk,” University of Chicago manuscript |

Citations: | 41 - 17 self |

### BibTeX

@ARTICLE{Anderson_aquartet,

author = {Evan W. Anderson and Lars Peter Hansen and Thomas J. Sargent},

title = {A Quartet of Semi-Groups for Model Specification, Detection, Robustness, and the Price of Risk},

journal = {Price of Risk,” University of Chicago manuscript},

year = {},

volume = {1},

pages = {68--123}

}

### Years of Citing Articles

### OpenURL

### Abstract

A representative agent fears that his model, a continuous time Markov process with jump and di#usion components, is misspecified and therefore uses robust control theory to make decisions. Under the decision maker's approximating model, that cautious behavior puts adjustments for model misspecification into factor prices for risk. We use a statistical theory of detection to quantify the appropriate amount of model misspecification that the decision maker should fear. Related semigroups describe (1) an approximating model; (2) the behavior of model detection statistics; (3) a model misspecification adjustment to the continuation value in the decision maker's Bellman equation; and (4) asset prices.