ESTIMATION OF BENEFIT RESERVES IN ENDOWMENT INSURANCE USING THE INDONESIAN MORTALITY TABLE IV AND ZILLMER METHOD
Abstract
This study focuses on determining the benefit reserves for endowment life insurance using the Zillmer method, an extension of the prospective reserve approach. Benefit reserves are crucial as they represent the funds insurance companies must set aside to cover future claims. Traditionally, reserves can be calculated retrospectively or prospectively. Still, the Zillmer method introduces an innovative approach by incorporating a Zillmer rate and time to account for loading costs, particularly at the beginning of the policy period. This research's novelty lies in applying the Zillmer method using the most recent Indonesian Mortality Table (TMI) IV, which provides updated and accurate life expectancy data for calculating reserves. The study reveals that the reserve values calculated using the Zillmer method are initially lower than those derived from the conventional prospective method due to the inclusion of the Zillmer rate. However, as the policy progresses, the reserve values gradually align with the prospective reserves after the Zillmer time period concludes. This study not only applies the Zillmer method in a local context with updated mortality data but also demonstrates how insurance companies can manage reserves more effectively, particularly in the early years of the policy.
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References
S. Bondarenko, N. Shlafman, N. Kuprina, O. Kalaman, O. Moravska, and N. Tsurkan, “PLANNING, ACCOUNTING AND CONTROL AS RISK MANAGEMENT TOOLS FOR SMALL BUSINESS INVESTMENT PROJECTS,” Emerging Science Journal, vol. 5, no. 5, pp. 650–666, Oct. 2021, doi: https://doi.org/10.28991/esj-2021-01302 .
N. Nadilia, N. Fitriyati, and I. Fauziah, “THE CONSTANT ANNUAL PREMIUM AND BENEFIT RESERVE FOR FOUR PARTICIPANTS IN JOINT LIFE INSURANCE,” InPrime: Indonesian Journal of Pure and Applied Mathematics, vol. 2, no. 2, pp. 97–104, Jun. 2020, doi: https://doi.org/10.15408/inprime.v2i2.14780 .
N. Aryanti and D. Ahmad, “PENENTUAN CADANGAN PREMI TAHUNAN RETROSPEKTIF ASURANSI JIWA DWIGUNA KASUS JOINT LIFE DENGAN MENGGUNAKAN METODE FACKLER,” Journal of Mathematics UNP, vol. 5, no. 1, pp. 55–58, Jul. 2020, doi: https://doi.org/10.24036/UNPJOMATH.V5I1.8911.
A. R. Effendie, MATEMATIKA AKTUARIA DENGAN MENGGUNAKAN SOFTWARE R. Yogyakarta: UGM PRESS - Badan Penerbit dan Publikasi Universitas Gadjah Mada, 2021. Accessed: Jan. 09, 2025. [Online]. Available: https://ugmpress.ugm.ac.id/en/product/statistika/matematika-aktuaria-dengan-menggunakan-software-r
Hasriati, H. Sirait, A. Prabowo, Sukono, and A. T. Bon, “LIFE INSURANCE PREMIUMS DWIGUNA JOINT LIFE AND LAST SURVIVOR WITH MAKEHAM LAW,” Proceedings of the International Conference on Industrial Engineering and Operations Management, pp. 3270–3279, 2021, doi: https://doi.org/10.46254/AN11.20210594.
N. L. Bowers, H. U. Gerber, J. C. Hickman, D. A. Jones, and C. J. Nesbitt, ACTUARIAL MATHEMATICS. Society of Actuaries, 1997.
H. Hasriati, S. Sukono, I. Hasbiyati, T. P. Nababan, and A. Kirana, “DWIGUNA LIFE INSURANCE ZILMER RESERVES WITH THE COX-INGERSOLL-ROSS (CIR) INTEREST RATE,” Komputasi: Jurnal Ilmiah Ilmu Komputer dan Matematika, vol. 20, no. 1, pp. 1–11, Dec. 2022, doi: https://doi.org/10.33751/komputasi.v1i1.6229.
R. Riaman, S. Supian, S. Sukono, and A. T. Bon, “MODELING OF PREMIUM RESERVES USING THE FACKLER METHOD IN EQUITY-LINKED LIFE INSURANCE,” in Proceedings of the 5th NA International Conference on Industrial Engineering and Operations Management Detroit, Michigan: IEOM Society, Aug. 2020. doi: https://doi.org/10.46254/NA05.20200504.
E. Anastasya Prionggo, M. Nabil Pratama, F. Indrayatna, U. Padjajaran, R. Bandung Sumedang Street Km, and J. Sumedang, “ESTIMATION OF PROSPECTIVE BENEFIT RESERVE BASED ON GROSS PREMIUM VALUATION METHOD USING INDONESIAN MORTALITY TABLE IV AND DE-MOIVRE ASSUMPTIONS,” Enthusiastic : International Journal of Applied Statistics and Data Science, pp. 56–67, Oct. 2022, doi: https://doi.org/10.20885/enthusiastic.vol2.iss2.art1.
T. Futami, MATEMATIKA ASURANSI JIWA, BAGIAN 1. Incorporated Foundation, Oriental Life Insurance Cultural Development Center, 1993.
M. Johny, B. Purwoko, and E. E. Merawaty, “EFFECT OF GROSS PREMIUMS, CLAIMS RESERVES, PREMIUM RESERVES, AND PAYMENT OF CLAIMS TO ROA,” International Journal of Economics, Management, Business, and Social Science, vol. 1, no. 1, pp. 31–43, Jan. 2021, doi: https://doi.org/10.59889/IJEMBIS.V1I1.6.
Destriani, N. Satyahadewi, and M. N. Mara, “PENENTUAN NILAI CADANGAN PROSPEKTIF PADA ASURANSI JIWA SEUMUR HIDUP MENGGUNAKAN METODE NEW JERSEY,” Bimaster : Buletin Ilmiah Matematika, Statistika dan Terapannya, vol. 3, no. 01, pp. 7–12, Feb. 2014, doi: https://doi.org/10.26418/BBIMST.V3I01.4462.
R. H. A. Lubis, R. S. Tobing, and Y. K. A. Piliang, “CALCULATION OF WHOLE LIFE INSURANCE PREMIUM RESERVES USING THE CANADIAN METHOD,” CGANT Journal of Mathematics and Applications, vol. 5, no. 2, pp. 159–170, Dec. 2024, doi: https://doi.org/10.25037/CGANTJMA.V5I2.174.
Ruhiyat, M. A. M. Aslam, and I. G. P. Purnaba, “CONTINGENT LIFE INSURANCE PREMIUM AND POLICY VALUE USING GAMMA-GOMPERTZ MORTALITY DISTRIBUTION MODEL,” AIP Conf Proc, vol. 3201, no. 1, Nov. 2024, doi: https://doi.org/10.1063/5.0230592.
Z. Zulfadri, A. Arnellis, and M. Subhan, “MODIFIKASI CADANGAN PREMI PROSPEKTIF PADA ASURANSI JIWA SEUMUR HIDUP JOINT LIFE MENGGUNAKAN METODE NEW JERSEY,” Journal of Mathematics UNP, vol. 4, no. 4, Dec. 2019, doi: https://doi.org/10.25077/jmu.4.3.1-6.2015.
R. Widia and M. Subhan, “PENERAPAN HUKUM WEIBULL PADA METODE NEW JERSEY DALAM PENENTUAN CADANGAN PREMI ASURANSI DWIGUNA STATUS JOINT LIFE,” Journal of Mathematics UNP, vol. 4, no. 3, Dec. 2019, doi: 10.24036/UNPJOMATH.V4I3.7195.
F. S. Ibrahim and D. Murni, “PENENTUAN CADANGAN PREMI PADA ASURANSI JIWA BERJANGKA STATUS JOINT LIFE MENGGUNAKAN METODE CANADIAN,” Journal of Mathematics UNP, vol. 7, no. 1, pp. 19–27, Mar. 2022, doi: https://doi.org/10.24036/unpjomath.v7i1.10870.
H. Hasriati, S. Sukono, I. Hasbiyati, T. P. Nababan, and A. Kirana, “DWIGUNA LIFE INSURANCE ZILMER RESERVES WITH THE COX-INGERSOLL-ROSS (CIR) INTEREST RATE,” Komputasi: Jurnal Ilmiah Ilmu Komputer dan Matematika, vol. 20, no. 1, pp. 1–11, Dec. 2022, doi: https://doi.org/10.33751/komputasi.v1i1.6229.
G. Wettstein, A. H. Munnell, W. Hou, and N. Gok, “THE VALUE OF ANNUITIES,” SSRN Electronic Journal, Mar. 2021, doi: https://doi.org/10.2139/ssrn.3797822.
D. P. Sari and J. Jazwinarti, “ANUITAS LAST SURVIVOR UNTUK KASUS TIGA ORANG TERTANGGUNG,” Indonesian Journal of Mathematics and Natural Sciences, vol. 39, no. 1, pp. 70–77, 2016, doi: 10.15294/IJMNS.V39I1.7706.
A. A. Salim, ASURANSI DAN MANAJEMAN RESIKO. Jakarta: Grafindo Persada, 2007.
M. Subhan, AKTUARIA. Padang: Universitas Negeri Padang, 2017.
T. Futami, MATEMATIKA ASURANSI JIWA BAGIAN II. Tokyo: Incorporated Foundation Oriental Life Insurance Cultural Development., 1994.
M. R. Oktavian, D. Devianto, and F. Yanuar, “KAJIAN METODE ZILLMER, FULL PRELIMINARY TERM, DAN PREMIUM SUFFICIENCY DALAM MENENTUKAN CADANGAN PREMI PADA ASURANSI JIWA DWIGUNA,” Jurnal Matematika UNAND, vol. 3, no. 4, p. 160, 2014, doi: https://doi.org/10.25077/jmu.3.4.160-167.2014.
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