Putri, Marshanda Pradilla (2026) Perhitungan Estimasi Cadangan Klaim Menggunakan Mack's Chain Ladder Model, Generalized Linear Model Dengan Distribusi Gamma Dan Pendekatan Over-Dispersed Poisson. Other thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Penelitian ini bertujuan untuk mengestimasi cadangan klaim asuransi menggunakan tiga pendekatan, yaitu Mack's Chain Ladder Model, Generalized Linear Model dengan distribusi Gamma, dan Generalized Linear Model dengan pendekatan Over-Dispersed Poisson (ODP). Data yang digunakan merupakan data paid claims periode Januari 2022 hingga Agustus 2025 yang disusun dalam bentuk incremental dan cumulative run-off triangle. Data klaim asuransi umumnya bersifat positif, right-skewed, serta memiliki variansi yang meningkat seiring perkembangan klaim, sehingga mengindikasikan adanya overdispersi. Oleh karena itu, penelitian ini diawali dengan pengecekan overdispersi pada incremental dan cumulative run-off triangle, yang menunjukkan bahwa data klaim mengalami overdispersi secara signifikan. Nilai klaim yang sangat ekstrem pada incremental paid claims menyebabkan ketidakstabilan hubungan mean-variance, sehingga dilakukan log-transformation untuk menstabilkan variansi sebelum proses pemodelan. Estimasi cadangan klaim kemudian dilakukan menggunakan Mack's Chain Ladder Model sebagai metode stokastik klasik, Generalized Linear Model dengan distribusi Gamma, dan Generalized Linear Model dengan pendekatan Over-Dispersed Poisson (ODP). Estimasi parameter pada kedua model Generalized Linear Model dilakukan menggunakan metode Maximum Likelihood Estimation dengan algoritma Fisher Scoring. Hasil estimasi selanjutnya dikembalikan ke skala klaim asli melalui inverse log-transformation untuk memperoleh estimasi cadangan klaim dalam skala asli. Evaluasi kinerja ketiga metode dilakukan dengan membandingkan nilai prediction error menggunakan Root Mean Square Error (RMSE) dan Mean Absolute Percentage Error (MAPE). Hasil penelitian menunjukkan bahwa Generalized Linear Model dengan pendekatan Over-Dispersed Poisson (ODP) menghasilkan akurasi prediksi terbaik dengan nilai RMSE sebesar 9.601.482.666 dan MAPE sebesar 18,21629%, lebih rendah dibandingkan Mack's Chain Ladder Model yang menghasilkan RMSE sebesar 9.601.482.667 dan MAPE sebesar 18,21629%, serta Generalized Linear Model dengan distribusi Gamma dengan RMSE sebesar 9.700.166.460 dan MAPE sebesar 18,56507%. Hasil ini menunjukkan bahwa kemampuan Generalized Linear Model dengan pendekatan Over-Dispersed Poisson (ODP) yang dilakukan log-transformation¬ pada datanya dalam menangani overdispersi dan struktur variansi data klaim menjadikannya metode paling optimal dalam mengestimasi cadangan klaim pada data paid claims yang digunakan dalam penelitian ini.
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This study aims to estimate insurance claim reserves using three approaches, namely Mack’s Chain Ladder Model, the Generalized Linear Model with Gamma distribution, and the Generalized Linear Model with the Over-Dispersed Poisson (ODP) approach. The data used are paid claims data from January 2022 to August 2025, which are arranged in the form of incremental and cumulative run-off triangles. Insurance claim data are generally positive, right-skewed, and have variance that increases along the claim development, indicating the presence of overdispersion. Therefore, this study begins with an overdispersion check on the incremental and cumulative run-off triangles, which shows that the claim data experience significant overdispersion. Extremely large claim values in the incremental paid claims cause instability in the mean–variance relationship; therefore, log-transformation is applied to stabilize the variance prior to the modeling process. Claim reserve estimation is then conducted using Mack’s Chain Ladder Model as a classical stochastic method, the Generalized Linear Model with Gamma distribution, and the Generalized Linear Model with the Over-Dispersed Poisson (ODP) approach. Parameter estimation in both Generalized Linear Models is performed using the Maximum Likelihood Estimation method with the Fisher Scoring algorithm. The estimation results are then returned to the original claim scale through inverse log-transformation to obtain claim reserve estimates in the original scale. The performance evaluation of the three methods is conducted by comparing prediction error values using Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE). The results show that the Generalized Linear Model with the Over-Dispersed Poisson (ODP) approach produces the best predictive accuracy, with an RMSE value of 9,601,482,666 and a MAPE value of 18.21629%, which are lower than those of Mack’s Chain Ladder Model with an RMSE value of 9,601,482,667 and a MAPE value of 18.21629%, as well as the Generalized Linear Model with Gamma distribution with an RMSE value of 9,700,166,460 and a MAPE value of 18.56507%. These results indicate that the ability of the Generalized Linear Model with the Over-Dispersed Poisson (ODP) approach, which applies log-transformation to the data, to handle overdispersion and the variance structure of claim data makes it the most optimal method for estimating claim reserves in the paid claims data used in this study.
| Item Type: | Thesis (Other) |
|---|---|
| Uncontrolled Keywords: | Cadangan Klaim, Distribusi Gamma, Generalized Linear Model, Mack’s Chain-Ladder Model, Over-Dispersed Poisson Claim Reserves, Gamma Distribution, Generalized Linear Model, Mack’s Chain-Ladder Model, Over-Dispersed Poisson |
| Subjects: | Q Science > QA Mathematics > QA275 Theory of errors. Least squares. Including statistical inference. Error analysis (Mathematics) Q Science > QA Mathematics > QA276 Mathematical statistics. Time-series analysis. Failure time data analysis. Survival analysis (Biometry) Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression Q Science > QA Mathematics > QA401 Mathematical models. |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Actuaria > 94203-(S1) Undergraduate Thesis |
| Depositing User: | Marshanda Pradilla Putri Putri |
| Date Deposited: | 13 Jan 2026 05:46 |
| Last Modified: | 13 Jan 2026 09:09 |
| URI: | http://repository.its.ac.id/id/eprint/129552 |
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