The bounds of premium and a fuzzy insurance model under risk aversion utility preference

The potential loss is traditionally considered as a random variable. In recent years, the special risk insurances have developed gradually, but we cannot obtain enough historical data because of the new types of insurance products. Therefore, using probability to deal with these insurance problems has certain limitations. In this paper, the potential loss of insured is considered as a nonnegative fuzzy variable based on credibility theory. Firstly, we prove that the risk averse decision makers prefer a fixed risk more than a fuzzy risk having the same expected value. Then the feasible price area under fuzzy loss is discussed. Moreover, a fuzzy optimal insurance model is established and the stop loss insurance is proved to be the optimal policy for the risk averse decision makers. In addition, the equation for solving the optimal deductible is given. Finally, some numerical examples of special risk insurances are given to illustrate the use of the research conclusions.