Sets of Models and Prices of Uncertainty

Abstract

A decision maker constructs a convex set of nonnegative martingales to use as likelihood ratios that represent parametric alternatives to a baseline model and also non-parametric models statistically close to both the baseline model and the parametric alternatives. 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. We offer quantitative illustrations for baseline models of consumption dynamics that display long-run risk. We describe a set of parametric alternatives that generates countercyclical prices of uncertainty.