This paper proposes two mixed models to study a consumer?s optimal saving in the presence of two types of risk: income risk and background risk. In the first model, income risk is represented by a fuzzy number and background risk by a random variable. In the second model, income risk is represented by a random variable and background risk by a fuzzy number. For each model, three notions of precautionary savings are defined as indicators of the extra saving induced by income and background risk on the consumer?s optimal choice. In conclusion, we can characterize the conditions that allow for extra saving relative to optimal saving under certainty, even when a certain component of risk is modelled using fuzzy numbers.
A possibilistic and probabilistic approach to precautionary saving