Determination of Joint Life Term Insurance Premium Reserves Using the Prospective Method Based on the Cox-Ingersoll-Ross (CIR) Stochastic Interest Rate Model

Authors

  • Prihatin Sihotang Departement of Mathematics, Bengkulu University
  • Siska Yosmar Departement of Mathematics, Bengkulu University
  • Septri Damayanti Departement of Mathematics, Bengkulu University

DOI:

https://doi.org/10.20956/j.v22i3.48922

Keywords:

Joint Life Term Insurance, Premium Reserves, Cox-Ingersol-Ross (CIR), Prospective Method

Abstract

Premium reserves are the minimum funds that insurance companies are required to set aside to guarantee the fulfillment of long-term contractual obligations to policyholders in the future. Good management of premium reserves is very important to maintain the financial stability of insurance companies. This study aims to determine the premium reserves for joint life term life insurance using a prospective method based on the CIR model stochastic interest rate. This study uses a literature review method, with calculations based on the 2019 Indonesian Mortality Table (TMI) and historical BI interest rate data for estimating CIR model parameters. The calculation results show that premium reserves tend to increase at the beginning of the period and decrease towards the end of the period. Compared to fixed interest rates, premium reserves using CIR model interest rates are higher in each period.

Author Biographies

Siska Yosmar, Departement of Mathematics, Bengkulu University

Lecturer in Actuarial Mathematics in one of the Mathematics undergraduate programmes at Bengkulu University.

Septri Damayanti, Departement of Mathematics, Bengkulu University

Lecturer in Actuarial Mathematics in one of the Mathematics undergraduate programmes at Bengkulu University.

References

[1] Andres, H., 2025. Modelling and Validation of Real-World Economic Scenarios in Insurance: Taking Pathwise Properties Into Account. HAL Open Science. https://pastel.hal.science/tel-05045343.

[2] Arta, I. P. S., Satriawan, D. G., Bagiana, I. K., Loppies SP, Y., Shavab, F. A., Mala, C. M. F., Sayuti, A. M., Safitri, D. A., Berlianty, T., Julike, W., Wicaksono, G., Marietza, F., Kartawinata, B. R. & Utami, F., 2021. Manajemen Risiko. Widina Bhakti Persada, Bandung.

[3] Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A. & Nesbitt, J. C., 1997. Actuarial Mathematics. Society of Actuaries.

[4] Brigo, D. & Mercurio, D., 2006. Interest Rate Models – Theory and Practice. Springer.

[5] Dickson, D. C. M., Hardy, M. R. & Waters, H. R., 2009. Actuarial Mathematics for Life Contingent Risks. Cambridge University Press.

[6] Futami, T., 1994. Matematika Asuransi Jiwa Bagian II (diterjemahkan oleh: Herliyanto, G). Oriental Life Insurance Cultural Development Center, Terjemahan Dari: Seime Hoken Sugaku Gekan.

[7] Glasserman, P., 2003. Monte Carlo Methods in Financial Engineering. Springer, New York.

[8] Hasriati., Hasbiyati, I., Kirana, A. & Prabowo, A., 2022. Cadangan Zillmer dengan Distribusi Pareto dan Tingkat Suku Bunga Cox-Ingersoll-Ross. Jurnal Matematika, Sains, dan Teknologi, Vol. 23, No. 2, 80-92.

[9] Hasugian, I. A., Muhyi, K. & Firlidany, N., 2022. Simulasi Monte Carlo dalam Memprediksi Jumlah Pengiriman dan Total Pendapatan. Buletin Utama Teknik, Vol. 17, No. 2, 133-138.

[10] Hull, J. C., 2015, Options, Futures, and Other Derivatives, Ninth Edition. Pearson Education, Amerika Serikat.

[11] Jordan, C. W., 1991. Life Contingencies. The Society of Actuaries.

[12] Khairani, N., Elfitra. & Siregar, T. M., 2025. Building an E-Learning System Calculating Pension Funds Using the Cox Ingersoll Ross Interest Rate Model. Jurnal Penelitian Pendidikan IPA, Vol.11, No.2, 742-751.

[13] Limbong, M. M. Y., Rachmatin, D. & Priatna, B. A., 2022. Penerapan Model Tingkat Suku Bunga Cox Ingersoll Ross (CIR) dalam Menentukan Iuran Normal Pensiun. Jurnal EurekaMatika, Vol. 10, No. 2, 111-120.

[14] Machi, L. A. & Mc-Evoy, B. T., 2016. The Literature Review: Six Steps to Success, Third Edition. Corwin A Sage Publishing Company.

[15] Mariana, E., Apriliani, E. & Surjanto, S. D., 2015. Estimasi Parameter pada Model Suku Bunga Cox-Ingersoll-Ross (CIR) Menggunakan Kalman Filter untuk Menentukam Harga Zero Coupon Bond. Jurnal Sains dan Seni ITS, Vol. 4, No. 2, 2337-3520.

[16] Nishi, T. S. D., 2024. Perhitungan Cadangan Premi Prospektif Asuransij Iwa Berjangka Joint Life Dengan Hukum Mortalitas Gompertz. Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Brawijaya, Malang.

[17] Pangestu, I. W. D. & Mahrani, D., 2023. Analisis Besar Iuran Normal Metode Frozen Initial Liability dan Metode Entry Age Normal Menggunakan Tingkat Suku Bunga Cox-Ingersoll-Ross (CIR). Indonesian Journal of Applied Mathematics, Vol. 3, No. 2, 29-39.

[18] Promislow, S. D., 2015. Fundamentals of Actuarial Mathematics. John Wiley & Sons Ltd, Canada.

[19] Saragih, A.Y., Chandra, M., Hutabarat, R, FM., Manullang, S. & Farhana, N. A., 2024. Analisis Perbandingan Cadangan Premi Asuransi Jiwa Berjangka Menggunakan Metode Zillmer dan Fackler. Journal of Social Science Research, Vol. 4, No. 6, 902-911.

[20] Silalahi, R. B. & Budiarto, R., 2022. Nilai Premi Asuransi Jiwa Berjangka Single Life Model Cox-Ingersoll-Ross (CIR). Jurnal Statistika dan Matematika, Vol. 4, No. 1, 1-8.

[21] Sukanasih, NK., Widana, IN. & Jayanegara, K., 2018. Cadangan Premi Asuransi Joint Life dengan Suku Bunga Tetap dan Berubah Secara Stokastik. Jurnal Matematika, Vol. 7, No. 2, 79-87.

[22] Sulistyawati, Y. & Kartikasari, M. D., 2024. Implementasi Metode New Jersey dalam Perhitungan Cadangan Premi dengan Suku Bunga Stokastik dan Konstan. Jambura Journal of Mathematics, Vol. 6, No. 2, 131-139.

[23] Umami, R. L., 2023. Penentuan Premi Tahunan dan Cadangan Premi dengan Metode New Jersey Asuransi Endowment Status Joint Life Menggunakan Suku Bunga Stokastik. Fakultas Sains dan Teknologi, Universitas Islam Negeri Walisongo, Semarang.

[24] Yosmar, S., Hn Wijay anti, S. & Faisal, F., 2019. Penentuan Premi Asuransi Jiwa Berjangka dengan Bunga CIR dan Hukum Mortalita Weibull. Seminar Nasional Statistika, Vol. 8, 20-25.

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Published

2026-05-14

How to Cite

Sihotang, P., Yosmar, S., & Damayanti, S. (2026). Determination of Joint Life Term Insurance Premium Reserves Using the Prospective Method Based on the Cox-Ingersoll-Ross (CIR) Stochastic Interest Rate Model. Jurnal Matematika, Statistika Dan Komputasi, 22(3), 730–742. https://doi.org/10.20956/j.v22i3.48922

Issue

Vol. 22 No. 3 (2026): May 2026

Section

Research Articles

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