Scale-Invariant Uncertainty-Averse Preferences and Source-Dependent Constant Relative Risk Aversion
Preferences are defined over consumption that is contingent on a finite number of states representing a horse race (Knightian uncertainty) and a roulette (objective risk). The class of scale-invariant (SI) ambiguity-averse preferences, in a broad sense, is uniquely characterized by a multiple-prior utility representation. Adding a weak certainty independence axiom is shown to imply either unit CRRA toward roulette risk or SI maxmin expected-utility preferences. Removing the weak independence axiom but adding a separability assumption on preferences over pure horse-race bets leads to source-dependent constant-relative-risk-aversion expected utility with a higher CRRA assigned to horse-race uncertainty than to roulette risk. The multiple-prior representation in this case is shown to generalize entropic variational preferences. An appendix characterizes the functional forms associated with SI ambiguity-averse preferences in terms of suitable weak independence axioms in place of scale invariance.
Skiadas, Constantinos. 2013. Scale-Invariant Uncertainty-Averse Preferences and Source-Dependent Constant Relative Risk Aversion. Theoretical Economics. 8: 59-93.