Twisted probabilities, uncertainty, and prices

Lars Peter Hansen, Bálint Szőke, Lloyd S. Han, Thomas J. Sargent

    Research output: Contribution to journalArticlepeer-review


    A decision maker constructs a convex set of nonnegative martingales to use as likelihood ratios that represent alternatives that are statistically close to a decision maker's baseline model. The set is twisted to include some specific models of interest. Max–min expected utility over that set gives rise to equilibrium prices of model uncertainty expressed as worst-case distortions to drifts in a representative investor's baseline model. Three quantitative illustrations start with baseline models having exogenous long-run risks in technology shocks. These put endogenous long-run risks into consumption dynamics that differ in details that depend on how shocks affect returns to capital stocks. We describe sets of alternatives to a baseline model that generate countercyclical prices of uncertainty.

    Original languageEnglish (US)
    Pages (from-to)151-174
    Number of pages24
    JournalJournal of Econometrics
    Issue number1
    StatePublished - May 2020


    • Asset prices
    • Exponential quadratic stochastic discount factor
    • Relative entropy
    • Risk
    • Robustness
    • Uncertainty

    ASJC Scopus subject areas

    • Economics and Econometrics


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