Valuation Reveals Uncertainty

2026-06-28

AI Summary

This study addresses the identification and recovery of the underlying uncertainty structure from observable dynamic sublinear valuation rules. By introducing the notion of time consistency and integrating dynamic sublinear valuation theory with nonparametric statistical estimation, the authors establish—for the first time—that a finite set of valuation observations suffices to uniquely identify the uncertainty structure that generated them. This result challenges the long-standing view in economics that Knightian uncertainty is inherently unmeasurable, offering instead an explicit characterization and enabling valid statistical inference about the uncertainty structure. The work thus provides a tractable, nonparametric pathway for quantifying ambiguity in decision-theoretic and financial settings.

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.

Problem

• uncertainty
• valuation
• time consistency
• nonparametric estimation
• Knightian uncertainty

Innovation

• sublinear valuation
• uncertainty recovery
• time consistency
• nonparametric estimation
• Knightian uncertainty