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Twisted probabilities, uncertainty, and prices

Author

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

Abstract

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.

Suggested Citation

  • Hansen, Lars Peter & Szőke, Bálint & Han, Lloyd S. & Sargent, Thomas J., 2020. "Twisted probabilities, uncertainty, and prices," Journal of Econometrics, Elsevier, vol. 216(1), pages 151-174.
  • Handle: RePEc:eee:econom:v:216:y:2020:i:1:p:151-174
    DOI: 10.1016/j.jeconom.2020.01.011
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    References listed on IDEAS

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    Cited by:

    1. Hansen, Lars Peter & Sargent, Thomas J., 2022. "Structured ambiguity and model misspecification," Journal of Economic Theory, Elsevier, vol. 199(C).
    2. Szőke, Bálint, 2022. "Estimating robustness," Journal of Economic Theory, Elsevier, vol. 199(C).

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    More about this item

    Keywords

    Risk; Uncertainty; Relative entropy; Robustness; Asset prices; Exponential quadratic stochastic discount factor;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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