Mixed models for optimal saving with labor income risk and interest-rate risk.

In this paper, optimal saving models with two risk components are studied: the labor income risk and the interest rate risk. These risks can be modeled probabilistically by random variables or possibilistically by fuzzy numbers. In mixed models, one of the components is probabilistic and the other one is possibilistic. After the construction of two mixed models of optimal saving, several notions of precautionary saving are defined. These measure the variation in optimal saving level when moving from one model to another (usually by adding a risk component). The main results of the paper establish necessary and sufficient conditions on the positivity of different precautionary savings. (This means that the presence of new risks generates extra-saving.).