Ambiguity Measurement

Abstract

Ordering alternatives by their degree of ambiguity is a crucial element in decision processes in general and in asset pricing in particular. So far the literature has not provided an applicable measure of ambiguity allowing for such ordering. The current paper addresses this need by introducing a novel empirically applicable ambiguity measure derived from a new model of decision making under ambiguity, called shadow probability theory, in which probabilities of events are themselves random. In this model a complete distinction is attained between preferences and beliefs and between risk and ambiguity that enables the degree of ambiguity to be measured. The merits of the model are demonstrated by incorporating ambiguous probabilities into asset pricing and it is proved that the well defined ambiguity premium that the paper proposes can be measured empirically.

Keywords: ambiguity, ambiguity measure, ambiguity aversion, knightian uncertainty, shadow probability theory, choquet expected utility, cumulative prospect theory, ellsber paradox, ambiguity premium