A Theoretical Foundation of Ambiguity Measurement

Abstract

Ordering alternatives by their degree of ambiguity is crucial in economic and financial decision-making processes. To quantify the degree of ambiguity, this paper introduces an empirically-applicable, outcome-independent (up to a state space partition), risk-independent, and attitude-independent measure of ambiguity. In the presence of ambiguity, the Bayesian approach can be extended to uncertain probabilities such that aversion to ambiguity is defined as aversion to mean-preserving spreads in these probabilities. Thereby, the degree of ambiguity can be measured by the volatility of probabilities, just as the degree of risk can be measured by the volatility of outcomes. The applicability of this measure is demonstrated by incorporating ambiguity into an asset pricing model.

Keywords: Ambiguity Measure, Ambiguity Aversion, Knightian Uncertainty, Uncertain Probabilities, Ambiguity Premium

JEL Classification: D81, D83, G11, G12