Three representations of preferences with decreasing absolute uncertainty aversion

This paper axiomatizes a class of preferences displaying decreasing absolute uncertainty aversion, which allows a decision maker to be more willing to take uncertaintybearing behavior when he becomes wealthier. In our first main result, we obtain three equivalent representations. The first is a variation on the constraint criterion of Hansen and Sargent (2001). The other two generalize Gilboa and Schmeidler (1989)’s maxmin criterion and Maccheroni, Marinacci and Rustichini (2006)’s variational representation. This class, when restricted to preferences exhibiting constant absolute uncertainty aversion, is exactly Maccheroni, Marinacci and Rustichini (2006)’s variational preferences. In our second main result, we establish relationships among the representations for several important classes within variational preferences.