Pricing of minimum guarantees in life insurance contracts with fuzzy volatility

We propose a model for the pricing of the minimum guarantee option embedded in equity-linked life insurance policies under uncertainty of randomness and fuzziness. The future lifetime of the insured is modelled as a random variable and the asset price evolution is described using a fuzzy binomial-tree model. In order to deal with both randomness and fuzziness, we model the present value of liabilities as a fuzzy random variable. Our results can be used by the actuary to understand the incidence of the minimum guarantee on the premium and to define the appropriate coverage strategies. A numerical example illustrates how our methodology works.