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Using fuzzy random variables in life annuities pricing
Authors:Jorge de Andrés-Sánchez  Laura González-Vila Puchades
Institution:a Department of Business Administration, Faculty of Economics and Business Studies, Rovira i Virgili University, Av. de la Universitat 1, 43204 Reus, Spain
b Department of Economic, Financial and Actuarial Mathematics, Faculty of Economics and Business, University of Barcelona, Av. Diagonal 696, 08034 Barcelona, Spain
Abstract:This paper develops life annuity pricing with stochastic representation of mortality and fuzzy quantification of interest rates. We show that modelling the present value of annuities with fuzzy random variables allows quantifying their expected price and risk resulting from the uncertainty sources considered. So, we firstly describe fuzzy random variables and define some associated measures: the mathematical expectation, the variance, distribution function and quantiles. Secondly, we show several ways to estimate the discount rates to price annuities. Subsequently, the present value of life annuities is modelled with fuzzy random variables. We finally show how an actuary can quantify the price and the risk of a portfolio of annuities when their present value is given by means of fuzzy random variables.
Keywords:Economics  Finance  Life annuities  Fuzzy numbers  Fuzzy random variables
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