The Optimal Saving with Mixed Parameters

This paper proposes two mixed models to study optimal saving in the presence of two types of risk: income risk and background risk. In the first model the income risk is a fuzzy number and the background risk is a random variable. In the second model the income risk is a random variable and the background risk is a fuzzy number. For these models three notions of precautionary saving are defined as indicators of the changes induced by the income risk and the background risk on the choice of optimal saving.