Model State Space Generalized Extreme Value Mixture Autoregressive dengan Estimator Hybrid EM-Particle Filter

Lande, Chrisandi Rantegau (2025) Model State Space Generalized Extreme Value Mixture Autoregressive dengan Estimator Hybrid EM-Particle Filter. Doctoral thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Data klaim asuransi dalam bentuk run-off triangle, baik itu dari klaim yang terjadi maupun pembayaran klaim, digunakan untuk mengestimasi cadangan klaim, outstanding reserve, dan Incurred But Not Reported (IBNR). Salah satu pengembangan metode dilakukan dengan metode Bayesian menggunakan hasil dari metode Chain Ladder maupun metode Bornhuetter-Ferguson. Namun, keterbatasan data run-off triangle sering kali mengharuskan dilakukan transformasi ke data time series dan pemodelan dalam state space menggunakan Kalman filter, yang hanya berlaku untuk data linier dan berdistribusi Gaussian. Penelitian ini mengembangkan model Generalized Extreme Value Mixture Autoregressive (GEVMAR) yang bersifat nonlinier dan berdistribusi Generalized Extreme Value (GEV). Model terbaik dipilih melalui estimasi Expectation-Maximization (EM) dan Bayesian, dengan adjusted SNR tipe 2 sebagai ukuran kinerja. Selanjutnya, model GEVMAR dikembangkan menjadi State Space Generalized Extreme Value Mixture Autoregressive (SS-GEVMAR) untuk prediksi dan peramalan. Penelitian ini bertujuan memperoleh prediksi dan peramalan optimal dalam proses state space filtering serta mengembangkan algoritma komputasi berbasis hybrid EM-Particle Filter. Studi kasus menggunakan data IBNR yang menunjukkan volatilitas dan multimodalitas. Hasil penelitian membuktikan bahwa SS-GEVMAR memiliki performa prediksi terbaik, dengan akurasi 57,431% lebih tinggi dibandingkan State Space Gaussian Value Mixture Autoregressive (SS-GMAR) berdasarkan MAPE, serta peramalan 12,462% lebih akurat dibandingkan SS-GMAR. Dengan demikian, SS-GEVMAR terbukti lebih unggul dibandingkan SS-GMAR dalam menangani volatilitas dan multimodalitas pada data IBNR.
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Insurance claim data represented in the form of a run-off triangle serves as a critical tool for the estimation of claim reserves, outstanding reserves, and Incurred But Not Reported (IBNR) reserves. Among the sophisticated methodologies available, the Bayesian approach leverages outcomes derived from the Chain Ladder and Bornhuetter-Ferguson techniques. Nevertheless, the inherent limitations associated with run-off triangle data frequently necessitate its transformation into a time series format and subsequent modeling within a state space framework utilizing the Kalman filter, which is confined to data exhibiting linearity and a Gaussian distribution. The research unveils a Generalized Extreme Value Mixture Autoregressive (GEVMAR) model, recognized for its nonlinearity and connection to a Generalized Extreme Value (GEV) distribution. The optimal model is determined through estimation procedures utilizing both ExpectationMaximization (EM) and Bayesian methodologies, with the adjusted SNR Type 2 serving as the criterion for performance evaluation. Furthermore, the model is expanded into a State Space Generalized Extreme Value Mixture Autoregressive (SS-GEVMAR) framework to facilitate prediction and forecasting, employing a computational algorithm that integrates the hybrid EM-Particle Filter. A case study involving IBNR data, which is indicative of volatility and multimodality, is undertaken. The results highlight that SS-GEVMAR demonstrates a significantly enhanced predictive capability, achieving an accuracy that exceeds the State Space Gaussian Mixture Autoregressive (SS-GMAR) model by 57.431%, as assessed by the Mean Absolute Percentage Error (MAPE) metric. Additionally, SS-GEVMAR enhances forecasting precision by 12.462% in comparison to SSGMAR. Consequently, SS-GEVMAR is recognized as a more robust model than SS-GMAR with respect to its capability in representing the volatility and multimodal characteristics inherent in IBNR data.

Item Type:	Thesis (Doctoral)
Uncontrolled Keywords:	State space, mixture autoregressive, generalized extreme value, hybrid EM-particle filter
Subjects:	H Social Sciences > HA Statistics H Social Sciences > HA Statistics > HA30.3 Time-series analysis Q Science > QA Mathematics > QA274.2 Stochastic analysis
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49001-(S3) PhD Thesis
Depositing User:	Chrisandi Rantegau Lande
Date Deposited:	14 Feb 2025 08:57
Last Modified:	14 Feb 2025 08:57
URI:	http://repository.its.ac.id/id/eprint/118741

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