Exploring Multivariate Copula Models and Fuzzy Interest Rates in Assessing Family Annuity Products

Abstract

This research explores the development of a reversionary annuity product transformed into a family annuity covering three individuals: husband, wife, and children. The innovative design of this product considers the sequencing of annuity payments post-participant's demise, aiming to mitigate the risk of parents' death impacting their children. Recognizing the inadequacy of assuming independence among individuals in premium calculations, the study employs a multivariate Archimedean Copula model to account for interdependence. The primary objective is to compute the survival single-life function for each individual taken from TMI IV 2009. Then the copula model is implemented with Clayton and Frank copulas at varying Kendall’s tau values (0.25, 0.5, and 0.75). Meanwhile, the interest rates are modeled using the BI-7-day (reverse) rate with a Triangular Fuzzy α-cut. The findings reveal that increasing Kendall’s tau values lead to higher pure premiums, and notably, the Frank Copula model yields higher premium values than the Clayton Copula model. This research contributes valuable insights into the actuarial assessment of family annuity products, shedding light on the significance of considering dependencies among individuals for more accurate premium calculations.