Research Publication

A decision maker constructs a convex set of nonnegative martingales to use as likeli-hood 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 con-sumption 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.

Keywords— Risk, uncertainty, relative entropy, robustness, asset prices, exponential quadratic stochastic discount factor

JEL Classification— C52, C58, D81, D84, G12

Paper

Associated Paper Results and Code

@article{hansen2020twisted,
  title={Twisted probabilities, uncertainty, and prices},
  author={Hansen, Lars Peter and Sz{\H{o}}ke, B{\'a}lint and Han, Lloyd S and Sargent, Thomas J},
  journal={Journal of Econometrics},
  volume={216},
  number={1},
  pages={151--174},
  year={2020},
  publisher={Elsevier}
}