Proper prudence, standard prudence and precautionary vulnerability

Adding risks is an important area in decision making under uncertainty, as it is rarely the case that people face only one single source of risk. In this context, Pratt and Zeckhauser [Econometrica 55 (1987) 143], Kimball [Econometrica 61 (1993) 589] and Gollier and Pratt [Econometrica 64 (1996) 1109] define the concepts of proper risk aversion, standard risk aversion and risk vulnerability. In this paper, we assume that the agent expects two independent, risky incomes in the future and focus on his precautionary saving motive or equivalently consumption behavior at time zero. This framework allows for a natural extension of the above papers and for the definition of new concepts that we call proper prudence, standard prudence and precautionary vulnerability.