# Optimal prevention with possibilistic and mixed background risk

## TL;DR

This paper investigates how possibilistic and mixed background risks influence optimal prevention levels across various models, extending prior probabilistic risk results with new necessary and sufficient conditions.

## Contribution

It provides necessary and sufficient conditions for prevention level changes under possibilistic and mixed background risks, expanding existing probabilistic risk analysis.

## Key findings

- Optimal prevention can increase or decrease depending on background risk type.
- Conditions identified that determine prevention level adjustments.
- Complements previous probabilistic risk results with possibilistic and mixed models.

## Abstract

In this paper the effect of posibilistic or mixed background risk on the level of optimal prevention is studied. In the framework of five purely possibilistic or mixed models, necessary and sufficient conditions are found such that the level of optimal saving decreases or increases as a result of the actions of various types of background risk. This way our results complete those obtained by Courbage and Rey for some prevention models with probabilistic background risk.