# The interest rate for saving as a possibilistic risk

## TL;DR

This paper develops a model for optimal saving where interest rate risk is represented as a fuzzy number, introducing possibilistic expected utility and analyzing how this risk influences saving behavior.

## Contribution

It introduces a possibilistic framework for modeling interest rate risk in saving, extending classical probabilistic models with new conditions for extra-saving behavior.

## Key findings

- Possibilistic interest-rate risk can induce extra-saving.
- A necessary and sufficient condition links risk presence to increased saving.
- Transitioning from probabilistic to possibilistic risk affects optimal saving levels.

## Abstract

In the paper there is studied an optimal saving model in which the interest-rate risk for saving is a fuzzy number. The total utility of consumption is defined by using a concept of possibilistic expected utility. A notion of possibilistic precautionary saving is introduced as a measure of the variation of optimal saving level when moving from a sure saving model to a possibilistic risk model. A first result establishes a necessary and sufficient condition that the presence of a possibilistic interest-rate risk generates an extra-saving. This result can be seen as a possibilistic version of a Rothschilld and Stiglitz theorem on a probabilistic model of saving. A second result of the paper studies the variation of the optimal saving level when moving from a probabilistic model (the interest-rate risk is a random variable) to a possibilistic model (the interest-rate risk is a fuzzy number).