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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika)
Deautama, Randi
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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THE BENEFITS OF FAMILY ANNUITY CALCULATION WITH VINE’S COPULA AND FUZZY INTEREST RATE Sari, Kurnia Novita; Deautama, Randi; Febrisutisyanto, Ady
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 4 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss4pp2461-2470

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.
Exploring Multivariate Copula Models and Fuzzy Interest Rates in Assessing Family Annuity Products Sari, Kurnia Novita; Febrisutisyanto, Ady; Deautama, Randi; Azirah, Nursiti; Mahani, Pida
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.17467

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.
Co-Authors Azirah, Nursiti Febrisutisyanto, Ady KURNIA NOVITA SARI Mahani, Pida