Size-of-risk aversion, time varying utility and healthy behaviours

In the context of time varying utility of wealth, this paper analyzes risk behavior in the case of a Decision Maker who can differently act as a Buyer or a Seller in order to study the appealing concept of size-of-risk attitude. Sufficient conditions ensuring existence and regularity of the proposed definitions are presented, both in the case of temporal size-of-risk aversion both in the case of instantaneous size-of-risk aversion. Sufficient conditions ensuring such behaviors are then investigated.