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All Journal International Journal of Quantitative Research and Modeling
Lulu Ulmufidah
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Computer Science & IT Decision Sciences, Operations Research & Management Engineering Environmental Science Physics

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Bankruptcy Probability Modeling Using Integro-Differential Equations With Gamma Distributed Claims Lulu Ulmufidah; Agung Prabowo; Niken Larasati
International Journal of Quantitative Research and Modeling Vol. 7 No. 2 (2026): International Journal of Quantitative Research and Modeling (IJQRM)
Publisher : Research Collaboration Community (RCC)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46336/ijqrm.v7i2.1329

Abstract

This study aims to model and analyze the ruin probability of an insurance company using an integro-differential equation under the assumption that claim sizes follow a Gamma distribution. The research method employed is a literature study, conducted by reviewing relevant books and scientific articles. The modeling process is carried out using an integro-differential equation and simplifying it into the form of a homogeneous linear differential equation. Numerical computations are performed using Python programming, and the results are presented in tables and graphs to facilitate analysis. The model is developed in four cases based on variations in the parameters of the Gamma distribution. The results show that the ruin probability decreases as the initial capital and premium loading increase, and increases as the expected value of claims rises. Therefore, an increase in the insurance company’s surplus will reduce the risk of ruin.
Co-Authors Agung Prabowo Niken Larasati