Life settlement pricing with fuzzy parameters

Existing literature asserts that the growth of life settlement (LS) markets, where they exist, is hampered by limited policyholder participation and suggests that to foster this growth appropriate pricing of LS transactions is crucial. The pricing of LSs relies on quantifying two key variables: the insured's mortality multiplier and the internal rate of return (IRR). However, the available information on these parameters is often scarce and vague. To address this issue, this article proposes a novel framework that models these variables using triangular fuzzy numbers (TFNs). This modelling approach aligns with how mortality multiplier and IRR data are typically provided in insurance markets and has the advantage of offering a natural interpretation for practitioners. When both the mortality multiplier and the IRR are represented as TFNs, the resulting LS price becomes a FN that no longer retains the triangular shape. Therefore, the paper introduces three alternative triangular approximations to simplify computations and enhance interpretation of the price. Additionally, six criteria are proposed to evaluate the effectiveness of each approximation method. These criteria go beyond the typical approach of assessing the approximation quality to the FN itself. They also consider the usability and comprehensibility for financial analysts with no prior knowledge of FNs. In summary, the framework presented in this paper represents a significant advancement in LS pricing. By incorporating TFNs, offering several triangular approximations and proposing goodness criteria of them, it addresses the challenges posed by limited and vague data, while also considering the practical needs of industry practitioners

A Possibilistic Approach to Evaluating Equity-Linked Life Insurance Policies

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