Analysis of Ruin Probability in Insurance Companies Using the Cramer-Lundberg Model with Variations in Claim Distributions

Khairiati, Alfi (Institut Sains dan Teknologi Nasional Jakarta)
Budiarti, Retno (Department Mathematics, IPB University)
Najib, Mohamad Khoirun (Department Mathematics, IPB University)

Zero : Jurnal Sains, Matematika, dan Terapan
Vol 9, No 2 (2025): Zero: Jurnal Sains Matematika dan Terapan

Ruin risk is a critical concern in the insurance industry, reflecting a company’s ability to fulfill long-term claim obligations. This study estimates ruin probabilities using the Cramer-Lundberg model, with Monte Carlo simulation applied to three claim distributions: exponential, lognormal, and gamma. Simulations vary initial capital while holding the premium rate, claim intensity, and distribution parameters constant. Results show that the lognormal distribution, due to its heavy tail, leads to higher ruin probabilities compared to exponential and gamma distributions. The gamma distributions produce intermediate outcomes, while the exponential shows the lowest risk. These findings highlight the importance of considering distributional characteristics when assessing solvency risk. The study provides practical insights for actuaries and risk managers in evaluating capital adequacy, stress-testing portfolios, and developing adaptive pricing and reinsurance strategies.