A quartet of semigroups for model specification, robustness, prices of risk, and model detection

Evan W. Anderson, Lars Peter Hansen, Thomas Sargent

    Research output: Contribution to journalArticle

    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.

    Original languageEnglish (US)
    Pages (from-to)68-123
    Number of pages56
    JournalJournal of the European Economic Association
    Volume1
    Issue number1
    DOIs
    StatePublished - Mar 2003

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    Model specification
    Price of risk
    Robustness
    Decision maker
    Model misspecification
    Market price
    Markov process
    Risk factors
    Statistics
    Continuous time
    Uncertainty
    Robust control
    Control theory
    Asset prices
    Jump
    Bellman equation
    Representative agent

    ASJC Scopus subject areas

    • Economics, Econometrics and Finance(all)

    Cite this

    A quartet of semigroups for model specification, robustness, prices of risk, and model detection. / Anderson, Evan W.; Hansen, Lars Peter; Sargent, Thomas.

    In: Journal of the European Economic Association, Vol. 1, No. 1, 03.2003, p. 68-123.

    Research output: Contribution to journalArticle

    Anderson, Evan W. ; Hansen, Lars Peter ; Sargent, Thomas. / A quartet of semigroups for model specification, robustness, prices of risk, and model detection. In: Journal of the European Economic Association. 2003 ; Vol. 1, No. 1. pp. 68-123.
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