# RUIN PROBABILITY IN THE CLASSICAL RISK PROCESS WITH WEIBULL CLAIMS DISTRIBUTION

• Dadang Amir Hamzah Actuarial Science Study Program, Faculty of Business, President University, Indonesia https://orcid.org/0000-0002-1323-9278
• Theresia Stefany Anawa Siahaan Actuarial Science Study Program, Faculty of Business, President University, Indonesia
• Vania Chrestella Pranata Actuarial Science Study Program, Faculty of Business, President University, Indonesia
Keywords: Euler's method, Laplace Transform, Ruin Probability, Survival Probability, Trapezoid Rule, Weibull Distribution

### Abstract

In the classical risk process, ruin is the situation when the surplus falls below zero. Ruin probability is a tool used to predict bankruptcy in the insurance company. The ruin probability can be determined by solving the Integral-Differential equation that arises from the classical risk process. In this paper, we are interested in calculating the ruin probability when the claim distribution follows the Weibull distribution. Based on the Weibull parameter, the calculation is divided into two cases: when alpha equals 1 and when  . The Laplace transform gives the analytical solution of the Integral-Differential equation. However, when  the analytical solution cannot be determined since the Laplace transform is no longer applicable due to the presence of an improper integral that is not possible to solve analytically. Therefore, for the case alpha greater than 1, Euler’s method is applied to determine its numerical solution. The accuracy of the numerical solution is validated by comparing it with the analytical solution for the case  Then, using the accuracy determined from the first case, we apply the Euler method to determine the numerical solution for the case . The numerical method gives good accuracy to the analytical solution with the order of  calculated from  until

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Published
2023-12-19
How to Cite
[1]
D. Hamzah, T. Siahaan, and V. Pranata, “RUIN PROBABILITY IN THE CLASSICAL RISK PROCESS WITH WEIBULL CLAIMS DISTRIBUTION”, BAREKENG: J. Math. & App., vol. 17, no. 4, pp. 2351-2358, Dec. 2023.
Section
Articles