Analisis Estimasi Cadangan Klaim Pada Asuransi Umum Dengan Pendekatan Three-Part Robust Generalized Linear Model

Adam Adhitya Prayoga, Danang Teguh Qoyyimi, S.Si., M.Sc., Ph.D.

2026 | Skripsi | S1 ILMU AKTUARIA

Metode cadangan klaim konvensional seperti Chain Ladder pada umumnya dikembangkan untuk data agregat dengan periode pengamatan yang relatif panjang, seperti periode tahunan. Namun, ketika periode observasi diperpendek menjadi bulanan untuk memperoleh informasi yang lebih rinci mengenai dinamika arus kas klaim, muncul berbagai kompleksitas struktural yang tidak sepenuhnya dapat diakomodasi oleh pendekatan konvensional. Kompleksitas tersebut meliputi tingginya proporsi klaim bernilai nol (excess zero), kemunculan nilai klaim negatif akibat proses subrogasi dan salvage, serta keberadaan klaim ekstrem (outlier) yang dipicu oleh kejadian katastropik. Keterbatasan metode konvensional dalam menangani karakteristik tersebut mendorong pengembangan berbagai metode baru. Penelitian ini mengusulkan penggunaan metode Three-Part Robust Generalized Linear Model (Three-Part RGLM), yang merupakan sintesis dari arsitektur Three-Part Model dan kerangka kerja Robust Generalized Linear Model (RGLM). Three-Part Model mendekomposisi data klaim inkremental menjadi tiga komponen, yaitu model probabilitas klaim menggunakan distribusi Binomial, model besaran klaim nonpositif menggunakan distribusi Compound Poisson-Gamma, dan model besaran klaim positif menggunakan distribusi Lognormal. Sementara itu, sifat robust diperoleh melalui penggantian residual pearson pada fungsi skor Maximum Likelihood Estimation dengan fungsi Huber dalam kerangka M-Estimator yang diselesaikan secara iteratif menggunakan algoritma RIRLS. Metode ini kemudian diterapkan pada data klaim inkremental bulanan lini bisnis asuransi kendaraan bermotor dari salah satu perusahaan asuransi umum di Indonesia. Berdasarkan metrik evaluasi Root Mean Square Error (RMSE), Three-Part RGLM menghasilkan tingkat akurasi prediksi yang lebih baik dibandingkan metode konvensional Chain Ladder dan metode modern Extreme Gradient Boosting (XGBoost).

Conventional claim reserving methods such as Chain Ladder are generally developed for aggregated data with relatively long observation periods, such as annual data. However, when the observation period is shortened to a monthly basis in order to obtain more detailed information on claim cash flow dynamics, various structural complexities emerge that cannot be adequately accommodated by conventional approaches. These complexities include a high proportion of zero-valued claims (excess zeros), the occurrence of negative claim amounts due to subrogation and salvage processes, and the presence of extreme claims (outliers) caused by catastrophic events. The limitations of conventional methods in handling these characteristics have motivated the development of new methodologies. This study proposes the Three-Part Robust Generalized Linear Model (Three-Part RGLM), which combines the architecture of the Three-Part Model with the framework of the Robust Generalized Linear Model (RGLM). The Three-Part Model decomposes incremental claim data into three components: a claim occurrence model based on the Binomial distribution, a non-positive claim severity model based on the Compound Poisson-Gamma distribution, and a positive claim severity model based on the Lognormal distribution. Meanwhile, robustness is achieved by replacing the pearson residual in the score function of the Maximum Likelihood Estimation with the Huber function within the M-Estimation framework, which is solved iteratively using the RIRLS algorithm. The proposed method is applied to monthly incremental claim data from the motor insurance line of business of an Indonesian general insurance company. Based on the Root Mean Square Error (RMSE) evaluation metric, the Three-Part RGLM demonstrates superior predictive accuracy compared with the conventional Chain Ladder method and the modern Extreme Gradient Boosting (XGBoost) approach.

Kata Kunci : Cadangan klaim, Robust Generalized Linear Model, Three-Part Model.