Penentuan Retensi Optimal Reasuransi Stop-Loss Dengan Metode Optimasi Value at Risk ( VaR)

Amburasi, Ali Adam (2025) Penentuan Retensi Optimal Reasuransi Stop-Loss Dengan Metode Optimasi Value at Risk ( VaR). Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Penelitian ini bertujuan menentukan retensi optimal dalam reasuransi stop-loss dengan metode optimasi Value at Risk (VaR) untuk meningkatkan efisiensi manajemen risiko perusahaan asuransi. Data klaim riil dari perusahaan asuransi XYZ periode Juli 2020 Juni 2022 (430 observasi) dianalisis menggunakan empat distribusi probabilitas: Burr, Gamma, Log-logistik, dan Log-normal. Estimasi parameter dilakukan dengan Maximum Likelihood Estimation (MLE), diikuti uji validitas Anderson-Darling (AD) dan simulasi Monte Carlo untuk menentukan nilai kritis. Hasil menunjukkan Distribusi Gamma dengan parameter shape (α ̂=1.10274) dan scale ((β) ̂=57.92645) menjadi model terbaik meskipun tidak lolos uji statistik formal, karena relevansi visual dan kemampuan merepresentasikan risiko ekstrem. Berdasarkan teorema Cai & Tan (2007), retensi optimal (d^') ditentukan melalui invers fungsi survival pada tingkat safety loading (ρ=15%), menghasilkan d^'=98.5 juta. Premi reasuransi dihitung sebesar 8.68 juta dengan total VaR risiko 107.18 juta. Analisis sensitivitas mengungkapkan bahwa peningkatan safety loading mengurangi eksposur risiko perusahaan tetapi meningkatkan biaya reasuransi. Penelitian ini juga mengidentifikasi keterbatasan utama, termasuk ketergantungan pada asumsi distribusi dan ketiadaan faktor eksternal seperti inflasi. Kontribusi penelitian terletak pada integrasi metode VaR dengan model stop-loss untuk menyeimbangkan retensi dan transfer risiko. Hasil ini memberikan panduan praktis bagi perusahaan asuransi dalam merancang strategi reasuransi yang hemat biaya dan berkelanjutan. Rekomendasi untuk penelitian lanjutan mencakup penggunaan distribusi heavy-tailed misalnya Generalized Pareto Distribution (GPD) dan simulasi dinamika pasar untuk meningkatkan akurasi model.
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This study aims to determine the optimal retention in stop-loss reinsurance using the Value at Risk (VaR) optimization method to improve the efficiency of insurance company risk management. Real claims data from XYZ insurance company for the period July 2020 to June 2022 (430 observations) were analyzed using four probability distributions: Burr, Gamma, Log-logistic, and Log-normal. Parameter estimation is performed with Maximum Likelihood Estimation (MLE), followed by Anderson-Darling (AD) validity test and Monte Carlo simulation to determine critical values. Results show that the Gamma distribution with shape (α ̂=1.10274) and scale (β ̂=57.92645) parameters is the best model despite not passing formal statistical tests, due to its visual relevance and ability to represent extreme risks. Based on the theorem of Cai & Tan (2007), the optimal retention (d^') was determined through the inverse of the survival function at the safety loading level (ρ=15%) resulting in d^'=98.5 million. The reinsurance premium was calculated at 8.68 million with a total risk VaR of 107.18 million. Sensitivity analysis revealed that increasing safety loading reduced the company's risk exposure but increased the reinsurance costs. The study also identified key limitations, including the reliance on distribution assumptions and the absence of external factors such as inflation. The research contribution lies in the integration of the VaR method with the stop-loss model to balance retention and risk transfer. The results provide practical guidance for insurance companies in designing cost-effective and sustainable reinsurance strategies. Recommendations for further research include the use of heavy-tailed distributions such as Generalized Pareto Distribution (GPD) and market dynamics simulation to improve the accuracy of the model.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Manajemen risiko asuransi, Reasuransi, Retensi optimal, Stop-loss, Value at Risk (VaR). Insurance risk management, Reinsurance, Optimal retention, Stop-loss, Value at Risk (VaR)
Subjects:	H Social Sciences > HG Finance H Social Sciences > HG Finance > HG8054.5 Risk (Insurance) Q Science > QA Mathematics Q Science > QA Mathematics > QA276 Mathematical statistics. Time-series analysis. Failure time data analysis. Survival analysis (Biometry)
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Actuaria > 94203-(S1) Undergraduate Thesis
Depositing User:	Ali Adam Amburasi
Date Deposited:	14 Aug 2025 03:04
Last Modified:	14 Aug 2025 03:04
URI:	http://repository.its.ac.id/id/eprint/128097

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