Estimasi Cadangan Klaim IBNR: Pendekatan Metode Bornhuetter Ferguson dan Metode Munich Chain Ladder
Abstract
Estimating claim reserves in an insurance company is crucial. Inaccuracy of the estimation results can affect the condition of an insurance company. Thus, the estimation results are expected to be close to the actual claims of a company. The purpose of this study is to compare the estimation of claim reserves using the Bornhuetter Ferguson and Munich Chain Ladder methods. The Bornhuetter Ferguson method utilizes internal information in the form of claim data and external information in the form of earned premium (company income derived from premiums paid by the insured). The Munich Chain Ladder method is a development of the Chain Ladder method that considers the correlation element between incurred claim data and paid claim data. In this study, both methods are applied to calculate the claim reserves of an insurance company in Malaysia. The estimation results obtained are the Bornhuetter-Ferguson method produces an estimate of claim reserves of RM2668458000 in paid data and RM3026005600 in incurred data, while the Munich Chain Ladder method produces an estimate of claim reserves of RM2938886000 in paid data and RM2134746600 in incurred data.
Full text article
References
Alai, D. H., Merz, M., & Wüthrich, M. V. (2009). Mean Square Error of Prediction in the Bornhuetter–Ferguson Claims Reserving Method. Annals of Actuarial Science, 4(1), 7–31. https://doi.org/10.1017/S1748499500000580
Abiyyu, I. (2015). Proyeksi Cadangan Klaim dengan Metode Munich Chain-Ladder. Skripsi diterbitkan. Fakultas Matematika dan Ilmu Pengetahuan Alam, Institut Pertanian Bogor, Bogor.
Adijuwono, E. (2016). Estimasi Cadangan Klaim Pada Asuransi Kendaraan Bermotor Menggunakan Model Muncih Chain-Ladder (Studi Kasus: PT. RST). Tesis tidak diterbitkan. Fakultas Ekonomi dan Bisnis, Universitas Indonesia, Jakarta.
Azizah. (2021). Pemodelan Klaim Asuransi Menggunakan Pendekatan Bayesian dan Markov Chain Monte Carlo. Jurnal Kajian Matematika dan Aplikasinnya (JKMA), 2(2). 7-13.
D’Agostino, R. B., & Stephens, M. A. (1986). Goodness-of-Fit-Techniques (Vol. 68). Marcel Dekker, INC.
F. Seru, Azizah, and A. D. Saputro. (2021). Model Stokastik dengan Pendekatan Generalized Linear Model Untuk Mengestimasi Cadangan Klaim Incurred but Not Reported. Barekeng, 15(4), 607-6014.
Hibatullah, M. I. (2016). Prediksi Cadangan Klaim Asuransi dengan Metode Bornhuetter-Ferguson.
Hikmah, Y., & Hikmah, I. R. (2022). Perhitungan Cadangan Klaim dengan Metode Chain Ladder Menggunakan Excel dan Rstudio. MAP (Mathematics and Applications) Journal, 4(2), 122–131. https://doi.org/10.15548/map.v4i2.4837
Hossack, I., Pollar, J., & Zenwirth, B. (1999). Introductory Statistics with Applications in General Insurance. University of Cambridge Press.
J. Vaughan, E., & Vaughan, T. (2008). Fundamentals of Risk and Insurance (10th ed.). Wiley.
Krishnamoorthy, K. (2006). Handbook of Statistical Distributions with Applications. Chapman & Hall/CRC.
Mack T. (1993). Distribution-free calculation of the standard error of chain-ladder reserve estimates. Astin Bulletin. 23(2), 213-225.
Mack, T. (2006). Parameter Estimation for Bornhuetter/Ferguson.
Mack, T. (2008). The Prediction Error Of Bornhuetter/Ferguson. Astin Bulletin, 87–103. https://doi.org/10.2143/AST.38.1.2030404
Majid, A. B., Puspita, E., & Agustina, F. (2018). Penggunaan Metode Bornhuetter-Ferguson pada Peramalan Besar Cadangan Claims Asuransi. 6, 54–61.
Olofsson, M. (2006). Stochastic loss reserving testing the new guidelines from the Australian prudential regulation authority (APRA) on Swedish portfolio data using a bootstrap simulation and distribution-free method by Thomas Mack. Tesis diterbitkan. Stockholm University, Stockholm
Pratama, L. B. (2020). Perhitungan Cadangan Klaim dengan Menggunakan Metode Chain-Ladder dan Munich chain-ladder. Skripsi diterbitkan. Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Islam Indonesia, Yogyakarta.
Quarg, G., & Mack, T. (2004). Munich Chain Ladder: A Reserving Method that Reduces the Gap between IBNR Projections Based on Paid Losses and IBNR Projections Based on Incured Losses. Blätter DGVFM, 26, 597–630.
Riaman, R., Subartini, B., & Parmikanti, K. (2023). Penggunaan Metode Bornhuetter-Ferguson untuk Estimasi Cadangan Klaim. Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika, 4(2), 1328–1343. https://doi.org/10.46306/lb.v4i2.366
Riyadi, A. (2022). Analisis Estimasi Cadangan Klaim IBNR Pada Asuransi Kredit Menggunakan Metode Munich Chain Ladder dan Bornhuetter-Ferguson Pada PT. XYZ. Tesis tidak diterbitkan. Fakultas Ekonomi dan Bisnis, Univesitas Indonesia, Jakarta.
Saputra, I. G. C. D., Nurrohmah, S., & Sari, S. F. (2021). Claim reserving prediction with Bornhuetter-Ferguson method. IOP Publicing, 2. https://doi.org/10.1088/1742-6596/1725/1/012102
Schmidt, Z. (2008). The Bornhuetter-Ferguson Principle. Variance, 2(1), 0085–0110.
Tsai, C. C.-L., & Kim, S. (2022). Model mortality rates using property and casualty insurance reserving methods. Insurance: Mathematics and Economics, 106, 326–340. https://doi.org/10.1016/j.insmatheco.2022.07.007
Authors
Copyright (c) 2025 Azizah Azizah, Ardia Fatma Sari, Meidy Indhira Putri
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-NonCommercial 4.0 International License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work