Actuarial mathematics with fuzzy parameters; An application to collective pension plans

Two types of uncertainty are found in the actuarial valuation operations. One of them is related to the random laws but the other is unrelated to them. In the latter one the opinion of the experts plays an essential role. We understand this uncertainty must be dealt with by means of the fuzzy logic. Thus we will suppose that the uncertain quantity of the interest rates and future capital can be estimated by means of fuzzy numbers. Based on this we develop some important formulations of actuarial mathematics. We apply the aforementioned methodology to a Collective Pension Plan. We study how to determine the distribution of possibility of the percentage to deduct from each worker's wages if the aim of the plan is the payment of a pension equal to a fixed percentage of the wages at retirement age per year worked. Once this distribution of possibility is known, we analyse by means of fuzzy logic the decision to make. We also show how the use of such logic improves the analysis of sensibility.