Research Publication

December 2018 | Working Paper

Twisted Probabilities, Uncertainty and Prices

Lars Peter Hansen, Thomas J. Sargent, Balint Szoke and Lloyd S. Han

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

SSRN link

Tags: Financial Market Linkages to the Macroeconomy, Risk, Robustness and Ambiguity, Uncertainty and Valuation|Export BibTeX >
  title={Sets of Models and Prices of Uncertainty},
  author={Hansen, Lars P. and Sargent, Thomas J.},
  institution={National Bureau of Economic Research}