FAMILY TAKAFUL ANNUITY WITH COPULA DEPENDENCE AND FUZZYACTUARIAL MARGIN RATE - Deautama, Randi
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, whose annuity payments begin the following month after the lump sum contribution (premium) payment is made by the participant. The calculation of tanahud (the risk component of the contribution) is usually done by assuming the freedom of random variables for the remaining lifetime between the annuitants. However, this is not relevant to the actual situation because husband and wife, husband and child, and wife and child are dependent on each other for survival. This study takes this dependency into account when modeling the joint distribution of remaining life expectancy between the parties. The joint distribution of remaining life time between annuitants is modeled with an Archimedian Copula constructed from the marginal distribution of each annuitant, whose distribution follows the mortality values in the 2019 Indonesian Mortality Table IV extrapolated using mixtured mortality model called the HKK Model. This research also takes into account the actuarial margin rate using BI-7 day (reverse) repo rate data estimated with fuzzy sets. This calculation model is implemented in 4 (four) family takaful annuity product schemes to obtain the value of annuity benefits in accordance with the contributions paid by participants. The greater Kendall’s Tau (? ) value, the greater the annuity benefit value, with an increase of approximately 3%–4% against an increase in ? of 0.25 from the independent case (? = 0).