Muzaki, Muhamad Aufa (2026) Pemodelan Bayesian Hierarchical Gaussian Process Regression Pada Data Klaim Multilini Untuk Estimasi Liability For Incurred Claims Berdasarkan IFRS 17. Other thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Kewajiban klaim pada bisnis reasuransi umum mengandung tingkat ketidakpastian yang tinggi akibat keterlambatan pelaporan dan penyelesaian klaim, sehingga diperlukan pengukuran kewajiban yang andal dan berbasis risiko. Dalam kerangka International Financial Reporting Standard (IFRS) 17, kewajiban atas klaim yang telah terjadi direpresentasikan melalui Liability for Incurred Claims (LIC), yang terdiri atas Best Estimate Liability (BEL) dan Risk Adjustment (RA). Penelitian ini bertujuan mengestimasi BEL, mengukur RA, dan menentukan LIC menggunakan pendekatan Bayesian Hierarchical Gaussian Process Regression pada data multilini bisnis reasuransi umum. Data yang digunakan berupa cumulative paid loss development triangle dari tiga lini bisnis reasuransi umum Munich Re, yaitu properti, kredit, dan maritim, selama periode 2013–2024. Model diestimasi menggunakan Bayesian Hierarchical Gaussian Process Regression dengan input warping dan inferensi Hamiltonian Monte Carlo No-U-Turn Sampler (NUTS). Hasil penelitian menunjukkan bahwa model terbaik adalah Bayesian Hierarchical Gaussian Process Regression dengan struktur hierarki, parameterisasi non-centered, input warping, dan kernel Squared Exponential. Estimasi rata-rata BEL pada lini bisnis properti, kredit, dan maritim berturut-turut sebesar 8.303,21; 420,864; dan 779,975 juta Euro. Pengukuran RA menggunakan pendekatan Conditional Tail Expectation (CTE) menghasilkan nilai yang lebih besar dibandingkan Value at Risk (VaR) pada seluruh lini bisnis karena mempertimbangkan risiko pada bagian ekor distribusi (tail distribution). Pada lini bisnis properti diperoleh RA VaR₀,₇₅ sebesar 1.453,32 dan RA VaR₀,₈₈ sebesar 2.710,07, sedangkan RA CTE₀,₇₅ sebesar 3.073,15 dan RA CTE₀,₈₈ sebesar 4.143,64. Pada lini bisnis kredit diperoleh RA VaR₀,₇₅ sebesar 90,54, RA VaR₀,₈₈ sebesar 163,224, RA CTE₀,₇₅ sebesar 184,914, dan RA CTE₀,₈₈ sebesar 251,793. Pada lini bisnis maritim diperoleh RA VaR₀,₇₅ sebesar 101,976, RA VaR₀,₈₈ sebesar 194,858, RA CTE₀,₇₅ sebesar 212,791, dan RA CTE₀,₈₈ sebesar 290,329. Pada tingkat kepercayaan 75%, nilai LIC berbasis VaR pada lini bisnis properti, kredit, dan maritim berturut-turut sebesar 9.756,53; 511,404; dan 881,951 juta Euro, sedangkan LIC berbasis CTE berturut-turut sebesar 11.376,36; 605,778; dan 992,767 juta Euro. Pada tingkat kepercayaan 88%, nilai LIC berbasis VaR berturut-turut sebesar 11.013,28; 584,087; dan 974,833 juta Euro, sedangkan LIC berbasis CTE berturut-turut sebesar 12.446,85; 672,656; dan 1.070,30 juta Euro.
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General reinsurance claim liabilities involve a high degree of uncertainty due to delays in claim reporting and settlement, making reliable and risk-based liability measurement essential. Under the International Financial Reporting Standard (IFRS) 17 framework, liabilities arising from incurred claims are represented by Liability for Incurred Claims (LIC), which consists of Best Estimate Liability (BEL) and Risk Adjustment (RA). This study aims to estimate BEL, measure RA, and determine LIC using a Bayesian Hierarchical Gaussian Process Regression approach for multi-line general reinsurance business data. The dataset comprises cumulative paid loss development triangles from three Munich Re general reinsurance business lines—property, credit, and marine—for the period 2013–2024. The model is estimated using Bayesian Hierarchical Gaussian Process Regression with input warping and Hamiltonian Monte Carlo No-U-Turn Sampler (NUTS) inference. The results indicate that the best-performing model is a Bayesian Hierarchical Gaussian Process Regression with a hierarchical structure, non-centered parameterization, input warping, and a Squared Exponential kernel. The estimated mean BEL values for the property, credit, and marine business lines are 8,303.21, 420.864, and 779.975 million Euros, respectively. RA measurement using the Conditional Tail Expectation (CTE) approach produces higher values than Value at Risk (VaR) across all business lines because it accounts for risk in the tail of the distribution. For the property business line, the estimated RA values are VaR₀.₇₅ = 1,453.32 and VaR₀.₈₈ = 2,710.07, while CTE₀.₇₅ = 3,073.15 and CTE₀.₈₈ = 4,143.64. For the credit business line, the estimated values are VaR₀.₇₅ = 90.54, VaR₀.₈₈ = 163.224, CTE₀.₇₅ = 184.914, and CTE₀.₈₈ = 251.793. For the marine business line, the estimated values are VaR₀.₇₅ = 101.976, VaR₀.₈₈ = 194.858, CTE₀.₇₅ = 212.791, and CTE₀.₈₈ = 290.329. At the 75% confidence level, the VaR-based LIC values for the property, credit, and marine business lines are 9,756.53, 511.404, and 881.951 million Euros, respectively, while the corresponding CTE-based LIC values are 11,376.36, 605.778, and 992.767 million Euros. At the 88% confidence level, the VaR-based LIC values are 11,013.28, 584.087, and 974.833 million Euros, respectively, whereas the CTE-based LIC values are 12,446.85, 672.656, and 1,070.30 million Euros.
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