Incorporating fuzzy information in pricing substandard annuities

摘要

There is a growing interest in the insurance industry in offering substandard annuities. These annuities, based on medical underwriting, provide a greater pay out than the standard ones to those individuals who are expected to have a lower than average life expectancy. Medically underwritten annuities often involve imprecise or vague information about the individuals such as health status and lifestyle. To address this issue, this paper proposes two approaches based on Fuzzy Sets Theory tools. Firstly, in order to determine substandard annuity payments, fuzzy mortality factors (also known as mortality multipliers) are introduced. These fuzzy mortality factors, modelled by means of triangular fuzzy numbers, can be estimated using conventional statistical confidence intervals. Secondly, by designing a fuzzy inference system, we demonstrate how to obtain the substandard annuity payment based on imprecise or vague personal information about annuitants. Numerical applications based on Spanish mortality data are provided for illustration.