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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan Jambura Journal of Mathematics Jurnal Matematika UNAND Jurnal Statistika dan Aplikasinya Milang Journal of Mathematics and Its Applications Jurnal Matematika Integratif MILANG Journal of Mathematics and Its Applications Limits: Journal of Mathematics and Its Applications
Ruhiyat
IPB University
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Electrical & Electronics Engineering Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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PERBANDINGAN ESTIMASI PREMI KLAIM ASURANSI KESEHATAN BERDASARKAN WILAYAH DAN STATUS PEROKOK MENGGUNAKAN MODEL BÜHLMANN–STRAUB Berlian Setiawaty; Annisa Aulia Putri; Bagus Handoko; Dendy Aditya; Monica Dewi Putri Kusmana; Ruhiyat
MILANG Journal of Mathematics and Its Applications Vol. 22 No. 1 (2026): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.22.1.15-26

Abstract

Peningkatan klaim asuransi kesehatan menuntut perusahaan asuransi menetapkan premi yang lebih sesuai dengan tingkat risiko. Penelitian ini bertujuan untuk mengestimasi dan membandingkan premi kredibilitas murni pada portofolio asuransi kesehatan menggunakan model semiparametrik Bühlmann-Straub, dengan fokus pada kombinasi faktor risiko status perokok dan wilayah tempat tinggal. Data yang digunakan adalah data besar klaim asuransi kesehatan dari Kaggle tahun 2023 yang dikelompokkan menjadi empat kelompok berdasarkan status perokok, bukan perokok dan region yaitu Southeast dan Northeast. Data besar klaim keempat kelompok tersebut dimodelkan menggunakan sebaran lognormal dan Weibull. Hasil penelitian menunjukkan bahwa model kredibilitas Bühlmann–Straub efektif menghasilkan premi asuransi kesehatan yang lebih akurat pada portofolio heterogen, dengan status perokok terbukti menjadi faktor risiko paling dominan dibandingkan wilayah. Faktor kredibilitas (Z) yang dihasillkan sangat tinggi, berkisar pada 0,99, menandakan bahwa pengalaman klaim tiap kelompok dapat diandalkan dalam penentuan premi. Hasil estimasi premi akhir tertinggi diperoleh kelompok perokok di Southeast (34841,838), sedangkan yang terendah adalah bukan perokok di Southeast (8296,787).
MODELING THE AGGREGATE LOSS DISTRIBUTION IN MOTOR THIRD-PARTY LIABILITY INSURANCE USING MONTE CARLO SIMULATION Tajmahal Ghaza Antoni; Nur Rahmadani Ahmad; Viery Salsaputra Triana; Gemala Azzahra Ocan; Ruhiyat
Jurnal Statistika dan Aplikasinya Vol. 10 No. 1 (2026): Jurnal Statistika dan Aplikasinya
Publisher : LPPM Universitas Negeri Jakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21009/JSA.10101

Abstract

This study models the aggregate loss distribution for motor third-party liability insurance using Monte Carlo simulation. Aggregate loss estimation is essential because it depends on claim frequency and severity, which often exhibit overdispersion and heavy tails, making analytical solutions intractable and motivating simulation-based approaches for accurate tail-risk assessment. The objective of this study is to identify appropriate distributions for frequency and severity using French Motor Third-Party Liability (MTPL) insurance data and to construct the aggregate loss distribution through Monte Carlo simulation. The modeling procedure involves distribution selection, goodness-of-fit assessment using Chi-Square and Kolmogorov-Smirnov tests, graphical comparison, and model evaluation using the Akaike Information Criterion (AIC). The selected distributions are then combined to generate simulated aggregate losses, from which Value at Risk (VaR) and Tail Value at Risk (TVaR) are computed. The results show that the Zero-One-Two-Three Modified Negative Binomial (Z123M-NB) distribution provides the best fit for claim frequency, while the Burr XII distribution effectively represents claim severity. Monte Carlo simulation with 10 million iterations produces stable estimates of the aggregate loss mean and variance, and the estimated VaR at the 95%, 97.5%, and 99% confidence levels are 105.85, 1,506.61, and 3,629.14, with corresponding TVaR values of 4,122.93, 7,418.70, and 15,075.21, indicating substantial tail heaviness. The study is limited by the sensitivity of variance estimation under extreme severity values and the assumption of a continuous severity model. The novelty of this study lies in integrating the Z123M-NB frequency model with Burr XII severity within a Monte Carlo framework for real MTPL data, offering enhanced flexibility in modeling extreme aggregate losses.
Co-Authors A. D. GARNADI Adinda Ramadhanty ADIYATNO, F. Aini, Nadhira Fajri Annisa Aulia Putri Bagus Handoko Benediktus Nugroho Adi Wiyoto Berlian Setiawaty Dendy Aditya Elsie Ardelia Erliana, Windiani F. ADIYATNO F. HANUM Farida Hanum Fendy Septyanto Furlo Gilbert Godfrey GARNADI, A. D. Gemala Azzahra Ocan Hadi Sumarno Hadi Sumarno HANUM, F. I Gusti Putu Purnaba Indrya Adilla Istiadi, H. A. F. Jonathan Ryan Wilianto Kelvin Gunawan Kenzi Lamberto M. F. WARDHANA M. ILYAS M. Ilyas, M. Maharani, Mutiara Monica Dewi Putri Kusmana Muhammad Yusuf Sulaiman Muwafiqo Zamzami Dhuha N. K. Kutha Ardana Nur Rahmadani Ahmad NURDIATI, S. Nurfatimah Amany PERMANA, R. A. PRASETYO, W. R. A. PERMANA Raymond Raymond Retno Budiarti Rizalius Karunia S. A. UTOMO S. NURDIATI Sumarno, Hadi Syifa Fauzia Tajmahal Ghaza Antoni Teofilus Kevin Irawan UTOMO, S. A. Viery Salsaputra Triana W. PRASETYO WARDHANA, M. F. Wilianto, Jonathan Ryan Windiani Erliana Windiani Erliana Yuda Ardiansyah