CADANGAN ZILLMER DENGAN DISTRIBUSI PARETO DAN TINGKAT BUNGA COX-INGERSOLL-ROSS
Keywords: dwiguna life insurance, zillmer reserves, pareto distribution, cox-ingersoll-ross interest rate
Abstract
This article discusses Zillmer's reserves for endowment life insurance. Zillmer reserves are a type of modification of premium reserves which are calculated using prospective reserves and the Zillmer rate. In Zillmer reserves, loading which is the difference between gross premium and net premium in the first policy year is greater than standard loading, so the purpose of this research is to find a way to make the loading smaller. To achieve this goal, this article uses the Pareto distribution and the Cox-Ingersoll-Ross (CIR) interest rate model. Based on the illustration, even though in the first policy year there was still a negative loading, however, Zillmer's reserves have been increasing from time to time since the second policy year.
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References
Bijma, F., Jonker, M., & van der Vaart, A. W. (2017). An Introduction to Mathematical Statistics. Amsterdam University Press.
Chan, W. S., & Tse, Y. K. (2022). Financial Mathemtics for Actuaries. World Scientific Publishing Co. Pte. Ltd.
Dalpatadu, R. J., & Singh, A. K. (2015). Estimation of Parameters of the Pareto Distribution Using a Minimization Technique. International Journal of Applied Science and Technology, 5(4), 8–10.
Dewi, L., Satyahadewi, N., & Sulistianingsih, E. (2013). Penentuan Cadangan Premi pada Asuransi Jiwa Dwiguna dengan Metode Zillmer. Buletin Ilmiah Matematika, Statistika Dan Terapannya, 2(3), 155–162. http://dx.doi.org/10.26418/bbimst.v2i03.3858.
Dickson, C. D. M., Hardy, M. H., & Waters, H. R. (2020). Actuarial Mathematics for Life Contingent Risks (3rd ed.). Cambridge University Press.
Gupta, S. C., & Kapoor, V. K. (2020). Fundamental of Mathematical Statistics. (12th ed.). Sultan Chand and Son.
Hasriati, & Nababan, T. P. (2019). Private Premium of Endowment Last Survivor and Joint Life Insurance with Pareto Distribution. International Journal of Statistical Distribution and Applications, 4(5), 76–81. https://doi.org/10.11648/j.ijsd.20190504.11
Hasriati, Nababan, T. P., & Hasbiyati, I. (2020). Reserve of Life Insurance Prospective Dwiguna Joint Life and Last Survivor with Gompertz Law. Proceedings of the 2nd African International Conference on Industrial Engineering and Operations Management, 1567–1573.
Iriana, N., Purnamasari, I., & Nasution, Y. N. (2020). Penentuan Cadangan Premi Asuransi Jiwa Seumur Hidup Menggunakan Metode Zillmer. Jurnal Matematika, Statistika Dan Komputasi, 16(2), 219–225. https://doi.org/10.20956/jmsk.v16i2.8312
Kamil, I., Suherman, & Murni, D. (2021). Modifikasi Cadangan Premi Tahunan Retrospektif pada Asuransi Jiwa Berjangka Kasus Joint Life dengan Metode Zillmer. UNPjoMath, 4(2), 12–17. http://dx.doi.org/10.24036/unpjomath.v6i2.11553
Oktavian, M. R., Novinto, D., & Yanuar, F. (2014). Kajian Metode Zillmer, Full Preliminary Term, dan Premium Sufficiency dalam Menentukan Cadangan Premi pada Asuransi Jiwa Dwiguna. Jurnal Matematika UNAND, 3(4), 160–167. https://doi.org/10.25077/jmu.3.4.160-167.2014
Olivieri, A., & Pitacco, E. (2015). Introduction to Insurance Mathematics. Technical and Financial Features of Risk Transfer (2nd ed.). In International Publishing.
Rotar, V. I. (2015). Actuarial Models. The Mathematics of Insurance (2nd ed.). A Chapman & Hall Book.
Sharpe, J., & Juárez, M. A. (2021). Estimation of the Pareto and Related Distributions – A Reference-Intrinsic Approach. Communications in Statistics: Theory and Method, 50(23), 1–20. https://doi.org/10.1080/03610926.2021.1916826
Sidarto, K. A., Syamsuddin, M., & Sumarti, N. (2019). Matematika Keuangan. ITB Press.
Tsao, H. P. (2019). Evolutionary Mathematics And Science For Life Contingency Investigation. In Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM) (Vol. 1).
Utami, R. M., Hasriati, & Aziskhan. (2015). Cadangan Zillmer Status Hidup Gabungan dengan Asumsi Balducci. JOM FMIPA, 2(1), 321–331.
Warsono, Gustavia, E., Kurniasari, D., Amanto, & Antonio, Y. (2019). On the Comparison of the Methods of Parameter Estimation for Pareto Distribution. IOP Conf. Series: Journal of Physics: Conf. Series, 1338. https://doi.org/10.1088/1742-6596/1338/1/012042
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