Determination of value at risk as the threshold for motor vehicle insurance claims using the gamma distribution

Ardiyan Budiman; Wahri Irawan; Mochamad Indrajit Roy

doi:10.66256/permata.v2i1.47

Authors

Ardiyan Budiman Universitas Islam Negeri Sultan Maulana Hasanuddin Banten Author
Wahri Irawan Universitas Islam Negeri Sultan Maulana Hasanuddin Banten Author
Mochamad Indrajit Roy Universitas Islam Negeri Sultan Maulana Hasanuddin Banten Author

DOI:

https://doi.org/10.66256/permata.v2i1.47

Keywords:

Value at Risk, Gamma Distribution, Motor Vehicle Insurance, Insurance Claims

Abstract

The growth of motor vehicles in Indonesia has increased the risk of traffic accident losses, highlighting the need for accurate claim risk management by insurance companies. One approach to determining claim thresholds is Value-at-Risk (VaR). This study aims to estimate VaR as a claim threshold for motor vehicle insurance by modeling claim amounts using the Gamma distribution. The research methodology includes descriptive analysis of claim data, distribution selection, parameter estimation via maximum likelihood, and goodness-of-fit testing with the Kolmogorov–Smirnov test. The data consist of 113 paid claim amounts from motor vehicle insurance during the 2024–2025 period. The results indicate that the claim data are positive and right-skewed, making them suitable for modeling with a Gamma distribution with shape parameter α = 10.9073 and scale parameter θ = 0.5457. The calculated VaR values are 30.8716 at the 95% confidence level and 36.687 respectively levels.

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Author Biographies

Ardiyan Budiman, Universitas Islam Negeri Sultan Maulana Hasanuddin Banten

Department of Islamic Insurance, Faculty of Islamic Economics and Business,
Wahri Irawan, Universitas Islam Negeri Sultan Maulana Hasanuddin Banten

Department of Islamic Insurance, Faculty of Islamic Economics and Business
Mochamad Indrajit Roy, Universitas Islam Negeri Sultan Maulana Hasanuddin Banten

Department of Islamic Insurance, Faculty of Islamic Economics and Business

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