Precautionary saving with possibilistic background risk

This paper studies a mixed model of saving with three risks: labor income and interest rate risks are random variables and background risk is a fuzzy number. Two notions of precautionary saving are introduced, measuring the effect of these types of risk on optimal saving and necessary and sufficient conditions on their non-negativity are proved. This leads to two concepts of consumer´s prudence when new risk parameters are introduced. The main results of the paper characterize the two concepts of prudence by conditions of partial derivatives of consumer´s utility function.