One lottery over a vector outcome space is said to be riskier than another if every risk averse decision-maker prefers the latter to the former. We consider two other criteria for making such comparisons, one of which is a generalization of second-order stochastic dominance. Our main result is...

Given a utility defined on a Hilbert outcome space, we define at each outcome a generalized Arrow-Pratt (GAP) coefficient belonging to the Hilbert space. Comparing the risk aversion of such utilities using their GAP coefficients is equivalent to doing so in terms of other standard,...

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...

The central results of this paper are dualities between actions in a decision problem that are not strongly (resp., weakly) dominated over a state space and actions that are best (resp., internal-best) replies to a state. The results admit action and state spaces that are subsets of abstract...