Optimal Prevention with Possibilistic Background Risk

Possibility risk theory starts from the hypothesis that this is described by a fuzzy number and not by a random variable, as in the traditional probabilistic modeling. This paper is an attempt of possibilistic approach to risk management problem. In particular, the models proposed in this paper can be connected by the way the possibilistic risk influences the probability of a loss, the dimensions of the loss or both of them simultaneously considered (i.e. self-insurance, self-protection, or self-insurance-cum-protection). In the paper, there are studied two-period models of risk management in which the possibilistic risk may appear in the first period or in the second period. The main results of the paper establish necessary and sufficient conditions, or only sufficient, for the optimal management level effort to raise or to decrease as a result of adding such a possibilistic risk. Index Terms- Optimal prevention, possibility theory, precautionary saving, self-insurance