The Revealed Preference Theory of Hedging

Abstract

Gilboa and Schmeidler (1989) characterize an axiomatization for a preference relation over acts to explain the behavior of ambiguity averse decision-makers. We extend this axiomatization to define a preference relation over sets of acts which have the numerical representation given by U(A) = maxf∈A minp∈∆{ P s u(f(s))p(s)} where A is a compact, convex set of acts, u is a von Neumann-Morgenstern utility over outcomes, and ∆ is a compact and convex set of finitely additive probability measures over states of nature. As opposed to Gilboa and Schmeidler’s notion of hedging, which only allows decision-makers to hedge after the resolution of states, our preference relation and modified set of axioms allow a decision-maker to hedge before the resolution of states, in line with the view of Raiffa’s critique (1961). This representation shows that any set of acts under our preference relation, which allows the decision-maker to choose from convexified sets of options, is equivalent to its unique optimal choice.