Comparative Aversion to Vector-Valued Risks

The classical theory of comparative risk aversion shows the equivalence of various criteria for comparing the aversion of cardinal preferences to risks with real outcomes. Parts of this theory have been extended to outcomes in Euclidean spaces. We complete, unify and generalize this theory. Our general equivalence result admits outcomes in locally convex topological vector spaces. Our special equivalence result, which involves our generalized Arrow-Pratt (GAP) coefficient, admits outcomes in Hilbert spaces. These results significantly expand the range of applications of the theory by making admissible risks that are embodied in a large class of random processes, including widely-used Wiener-related processes and second-order processes. We use our results to predict the effects of differential risk aversion on the subjective valuations of financial assets with continuous random dividend processes. We also provide a theoretically well-grounded, yet computationally tractable, method for estimating the GAP coefficient