We deal with the problem of pricing equity-linked life insurance policies under uncertainty of randomness and fuzziness. Firstly, we propose an evaluation method for general life insurance, with stochastic representation of mortality and fuzzy quantification of financial present values, by defining the actuarial value of the liabilities as the expectation of a fuzzy random variable. Then, we apply the suggested methodology to the fair valuation of an equity-linked policy. In such a contract policyholder’s benefits are linked to the performance of a reference fund. We perform the risk neutral valuation in a fuzzy binomial-tree model. The crisp value of the policy is obtained by means of a “defuzzification method” based on possibilistic mean values. A numerical example illustrates how the proposed method allows the actuary to model the fuzziness in the parameters according to his subjective judgement.
A Possibilistic Approach to Evaluating Equity-Linked Life Insurance Policies
ANZILLI, Luca
2012-01-01
Abstract
We deal with the problem of pricing equity-linked life insurance policies under uncertainty of randomness and fuzziness. Firstly, we propose an evaluation method for general life insurance, with stochastic representation of mortality and fuzzy quantification of financial present values, by defining the actuarial value of the liabilities as the expectation of a fuzzy random variable. Then, we apply the suggested methodology to the fair valuation of an equity-linked policy. In such a contract policyholder’s benefits are linked to the performance of a reference fund. We perform the risk neutral valuation in a fuzzy binomial-tree model. The crisp value of the policy is obtained by means of a “defuzzification method” based on possibilistic mean values. A numerical example illustrates how the proposed method allows the actuary to model the fuzziness in the parameters according to his subjective judgement.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
