A fuzzy random variable approach to life insurance pricing

Abstract

This paper develops life insurance pricing with stochastic representation of mortality and fuzzy quantification of interest rates following the methodology by Andrés and González-Vila (2012). We show that modelling the present value of life insurance contracts with fuzzy random variables allows a well-founded quantification of their fair price and the risk resulting from the uncertainty of mortality and discounting rates. So, we firstly describe fuzzy random variables and define some associated measures: the mathematical expectation, the variance, distribution function and quantiles. Subsequently the present value of life insurance policies is modelled with fuzzy random variables. We finally show how an actuary can quantify the price and the risk of a life insurance portfolio when the contracts present value is given by fuzzy random variables. © 2012 Springer-Verlag Berlin Heidelberg.