Comparative risk aversion when the outcomes are vectors

Pratt (1964) and Yaari (1969) contain the classical results pertaining to the equivalence of various notions of comparative risk aversion of von Neumann-Morgenstern utilities in the setting with real-valued outcomes. Some of these results have been extended to the setting with outcomes in < n . We obtain ana-logues of the classical results in the setting with outcomes in ordered topological vector spaces when differentiability is not required, and in the setting with out-comes in ordered Hilbert spaces when differentiability is required, as is the case when we work with a vector-valued generalized notion of an Arrow-Pratt coeffi-cient.