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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan
Olivia, Agna
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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ESTIMATION OF VALUE AT RISK FOR GENERAL INSURANCE COMPANY STOCKS USING THE GARCH MODEL Nugraha, Edwin Setiawan; Olivia, Agna; Sudding, Fauziah Nur Fahirah; Lestari, Karunia Eka
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss2pp1071-1082

Abstract

Investment plays a crucial role in supporting economic development by allocating funds to generate future profits. Among various investment options, stock investment is widely popular. However, investors face the challenge of developing strategies to maximize returns while minimizing risks. Effective investment requires understanding the potential maximum risk of loss, known as Value at Risk (VaR). This research focuses on estimating VaR for four top general insurance companies in Indonesia: PT Lippo General Insurance Tbk (LPGI), PT Asuransi Tugu Pratama Indonesia Tbk (TUGU), PT Victoria Insurance Tbk (VINS), and PT Asuransi Dayin Mitra Tbk (ASDM). These companies were selected due to their leading positions in the industry. The Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model, an extension of the ARIMA method designed to handle volatility clustering, is utilized for VaR estimation. Results at confidence levels of 90%, 95%, and 99% reveal that VINS carries the highest risk, with a maximum VaR of IDR 2,848,710 at 99% confidence, while LPGI shows the lowest risk, with a maximum VaR of IDR 22,677. For TUGU, the maximum possible loss is IDR 517,589, and for ASDM, it is IDR 1,532,267. Backtesting confirms the reliability of the models, with some accepted at specific significance levels. Based on this analysis, the results can help investors make investment decisions that minimize potential losses, specifically in the four stocks analyzed.
APPLICATION OF THE RANDOM FOREST ALGORITHM FOR ESTIMATING CONDITIONAL VALUE AT RISK (CVAR) ON THE STOCK PORTFOLIO OF INSURANCE COMPANIES IN INDONESIA Purwanto, Purwanto; Olivia, Agna
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1693-1708

Abstract

This study aims to estimate Conditional Value at Risk (CVaR) for insurance company stock portfolios using a machine learning approach to improve the accuracy of financial risk measurement under extreme market conditions. The application of machine learning, particularly the Random Forest algorithm, is crucial for the Indonesian insurance sector, which faces increasing exposure to market volatility and uncertainty. The model predicts stock returns based on technical indicators such as moving averages, volatility, and lagged returns. The analysis uses historical data from ten insurance companies listed on the Indonesia Stock Exchange (IDX) for the period 2022–2025. To assess model performance, Mean Absolute Error (MAE), Mean Squared Error (MSE), and Kupiec backtesting are employed. The model produces CVaR estimates of 1.65% and 1.94% at the 95% and 99% confidence levels, respectively. It also achieves a low MAE of 0.006701 and MSE of 0.000091, indicating high estimation accuracy. The Kupiec test results further confirm the statistical reliability of the CVaR estimates. This study contributes methodologically by highlighting the effectiveness of non-parametric ensemble learning in financial risk modeling. The findings offer practical implications for insurance firms and portfolio managers in adopting adaptive, data-driven risk mitigation strategies, especially in volatile market environments.
Co-Authors Karunia Eka Lestari Nugraha, Edwin Setiawan Purwanto Purwanto Sudding, Fauziah Nur Fahirah