Valuation Reveals Uncertainty

Abstract

This paper studies the recovery of uncertainty from dynamic sublinear valuation rules. A robust valuation assigns each payoff its worst-case expected value across plausible models under uncertainty and induces a dynamic sublinear valuation rule. While valuation rules are observable in practice, the underlying uncertainty structure is latent. First, we show that the latent uncertainty structure can be identified from an observed valuation rule and provide an explicit procedure for recovering it. Second, we develop the notion of time consistency for uncertainty structures as the uncertainty-side counterpart of time consistency in valuation. Third, we characterize all time-consistent uncertainty structures that represent a given valuation rule. Finally, we develop nonparametric estimators for recovering uncertainty from limited valuation data. These results overturn the traditional Knightian view that uncertainty is inherently non-measurable. Indeed, valuation contains sufficient information to identify, characterize, and statistically recover the uncertainty structures that generate it.