The interest rate for saving as a possibilistic risk

The paper is concerned with a saving model in which the interest rate risk is a fuzzy number. Our model can be seen as a possibilistic variant of a saving model due to Rothschild and Stiglitz, in which the interest rate risk is a random variable. A notion of possibilistic precautionary saving is defined as a measure of the optimal saving variation when moving from a certain model to the possibilistic interest rate risk model. A first result of the paper characterizes the possibilistic precautionary saving (i.e. generating extra-saving) by an inequality in which the relative prudence index associated with the consumer’s utility function appears. A second result compares the level of optimal saving from the Rothschild and Stiglitz with the level of optimal saving from the possibilistic model from the paper. Finally, two propositions on the approximate calculation of possibilistic optimal saving are proved. The two approximate calculation procedures are illustrated for particular cases of utility functions and fuzzy numbers. •Saving model with interest rate as a possibilistic risk.•Necessary and sufficient conditions for generating extra saving.•The approximate calculus of optimal possibilistic saving.