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.