THE BENEFITS OF FAMILY ANNUITY CALCULATION WITH VINE’S COPULA AND FUZZY INTEREST RATE

Abstract

One example of a multiple life annuity product (covering more than one person) is a reversionary annuity, which is a life annuity product for two or more annuitants whose annuity payments will begin after one of the annuitants specified in the contract dies first until the other annuitant also dies. This type of annuity is modified into a family annuity consisting of husband, wife, and child. The marginal distribution is constructed from a combined model of several mortality models such as Heligman-Pollard, Costakis, and Kannisto-Makeham models to capture mortality at young and old ages.This study takes this dependency into account when modeling the joint distribution of remaining life expectancy between the parties. The joint distribution of remaining lifetime between annuitants is modeled with a Vine’s copula constructed from the marginal distribution of each annuitant. This research also takes account the actuarial margin rate using BI-7-day (reverse) repo rate data estimated with fuzzy sets. The annuity benefits calculation is assumed with some Kendall's tau () values. The result shows the value of annuity benefits increases as the value of  increases.