Risk aversion and relationships in model-free.

This paper belongs to the study of decision making under risk. We will be interested in modeling the behavior of decision makers (hereafter referred to as DM) when they are facing risky choices. We first introduce both the general framework of decision making problem under risk and the different models of choice under risk that are well recognized in the literature. Then, we review different concepts of some increase in risk and risk aversion that are valid independently of any representation. We will introduce two new forms of behaviors under risk namely weak weak risk aversion and anti-monotone risk aversion. Note that the latter is related to anti-comonotony (a concept investigated in Abouda, Aouani and Chateauneuf (2008)) and represents a halfway between monotone and weak risk aversion. Finally, we discuss the relationships -in model-free- among some of these behaviors.