Pemodelan Risiko Kerugian Agregat Klaim Program Jaminan Sosial BPJS Ketenagakerjaan Kota Surabaya Menggunakan Pendekatan Panjer Recursion dan Fast Fourier Transform (FFT)

Farid, Naufal Abdul (2026) Pemodelan Risiko Kerugian Agregat Klaim Program Jaminan Sosial BPJS Ketenagakerjaan Kota Surabaya Menggunakan Pendekatan Panjer Recursion dan Fast Fourier Transform (FFT). Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Program jaminan sosial BPJS Ketenagakerjaan menanggung risiko klaim yang signifikan terhadap keberlanjutan sistem, sehingga pemodelan distribusi kerugian agregat yang akurat menjadi krusial untuk evaluasi kewajiban manfaat dan manajemen risiko pada tingkat wilayah. Penelitian ini memodelkan distribusi kerugian agregat klaim Program Jaminan Kecelakaan Kerja (JKK) dan Jaminan Kematian (JKM) BPJS Ketenagakerjaan Kota Surabaya menggunakan Collective Risk Model (CRM), serta mengestimasi Value at Risk (VaR) dan Tail Value at Risk (TVaR) pada tingkat kepercayaan 90%, 95%, dan 99%. Data yang digunakan adalah klaim agregat bulanan periode Juli 2020 sampai Desember 2025 sebanyak 66 observasi. Distribusi frekuensi dipilih dari kandidat Binomial, Poisson, Binomial Negatif, dan Geometrik melalui uji Chi-Square serta kriteria Akaike Information Criterion (AIC) dan Bayesian Information Criterion (BIC). Distribusi severitas dipilih dari kandidat Gamma, Pareto, Weibull, Lognormal, Beta Scaled, dan Mixture Lognormal melalui uji Anderson-Darling berbasis parametric bootstrap. Distribusi agregat dikomputasi menggunakan Fast Fourier Transform (FFT) dengan exponential tilting dan Panjer Recursion pada grid diskretisasi terpadu. Hasil penelitian menunjukkan frekuensi klaim JKK paling sesuai dimodelkan dengan distribusi Geometrik dan JKM dengan Binomial Negatif, sedangkan severitas JKK dengan Mixture Lognormal dan JKM dengan Beta Scaled. Ekspektasi kerugian agregat bulanan adalah Rp10,36 miliar untuk JKK dan Rp5,35 miliar untuk JKM. FFT dan Panjer Recursion menghasilkan PMF agregat yang identik. Pada tingkat kepercayaan 99%, JKK memiliki VaR Rp47,64 miliar dan TVaR Rp57,49 miliar, sedangkan JKM memiliki VaR Rp13,91 miliar dan TVaR Rp15,80 miliar. Estimasi tersebut valid melalui backtesting historis dan robust terhadap analisis sensitivitas dan stress testing. Hasil penelitian memberikan gambaran kuantitatif risiko klaim agregat BPJS Ketenagakerjaan Kota Surabaya sebagai dasar analitis evaluasi kewajiban manfaat dan penguatan manajemen risiko pada tingkat wilayah.
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The social security programs administered by BPJS Ketenagakerjaan bear substantial claim risk affecting system sustainability, so accurate aggregate loss modeling is crucial for benefit liability evaluation and regional risk management. This study models the aggregate loss distribution of Work Accident Insurance (JKK) and Death Insurance (JKM) claims of BPJS Ketenagakerjaan Surabaya within the Collective Risk Model (CRM) framework, and estimates Value at Risk (VaR) and Tail Value at Risk (TVaR) at 90%, 95%, and 99% confidence levels. The data consist of 66 monthly aggregate claim observations from July 2020 to December 2025. Frequency distributions are selected from Binomial, Poisson, Negative Binomial, and Geometric candidates via the Chi-Square test and Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) criteria. Severity distributions are selected from Gamma, Pareto, Weibull, Lognormal, Beta Scaled, and Mixture Lognormal candidates via the Anderson-Darling test with parametric bootstrap. The aggregate distribution is computed using the Fast Fourier Transform (FFT) with exponential tilting and Panjer Recursion on a unified discretization grid. The results show that JKK claim frequency is best modeled by the Geometric distribution and JKM by the Negative Binomial, while JKK claim severity is best modeled by the Mixture Lognormal and JKM by the Beta Scaled. The expected monthly aggregate loss is IDR 10.36 billion for JKK and IDR 5.35 billion for JKM. FFT and Panjer Recursion yield identical aggregate PMFs at machine precision. At the 99% confidence level, JKK has a VaR of IDR 47.64 billion and TVaR of IDR 57.49 billion, while JKM has a VaR of IDR 13.91 billion and TVaR of IDR 15.80 billion. These estimates are validated by historical backtesting and proven robust to sensitivity analysis and stress testing. The findings provide a quantitative overview of aggregate claim risk at BPJS Ketenagakerjaan Surabaya as an analytical basis for benefit liability evaluation and risk management at the regional level.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Fast Fourier Transform, kerugian agregat, Panjer Recursion, Tail Value at Risk, Value at Risk, aggregate loss, Fast Fourier Transform, Panjer Recursion, Tail Value at Risk, Value at Risk
Subjects:	H Social Sciences > HG Finance > HG8054.5 Risk (Insurance) Q Science > QA Mathematics Q Science > QA Mathematics > QA274.2 Stochastic analysis Q Science > QA Mathematics > QA404 Fourier series
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Actuaria > 94203-(S1) Undergraduate Thesis
Depositing User:	Naufal Abdul Farid
Date Deposited:	17 Jul 2026 04:19
Last Modified:	17 Jul 2026 04:19
URI:	http://repository.its.ac.id/id/eprint/135273

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