In the Erlang(2) risk process, ruin occurs when the surplus falls below zero, indicating potential bankruptcy for the insurance company. Predicting bankruptcy is crucial, and ruin probability serves as a key metric for this purpose. It involves solving an Integral-Differential equation derived from the Erlang(2) risk process. This study focuses on computing ruin probability under the assumption of a Weibull claim distribution. The analysis is divided into two scenarios based on the Weibull parameter: when  equals 1 and when it differs. While the Laplace transform offers an analytical solution for the Integral-Differential equation, its applicability diminishes when faced with an improper integral that defies analytical resolution. Consequently, for  greater than 1, finite difference method is employed to obtain a numerical solution. The accuracy of this numerical approach is verified by comparing it against the analytical solution when  equals 1. Subsequently, leveraging the accuracy established in the first scenario, the finite difference method is applied to compute the numerical solution for the differing  scenario. The numerical method is satisfactory when calculated from u = 0 to u = 100, matching the analytical solution.

finite difference method, Laplace transform, ruin probability, trapezoid rule, Weibull distribution.

Received: April 12, 2024;  Accepted: May 27, 2024; Published: June 5, 2024

How to cite this article: Delwendé Abdoul-Kabir KAFANDO, Kiswendsida Mahamoudou OUEDRAOGO, Lassané SAWADOGO and Souleymane SAWADOGO, Numerical methods applied to ruin probability in an Erlang(2) risk process with Weibull loss distribution, International Journal of Numerical Methods and Applications 24(2) (2024), 109-125. https://doi.org/10.17654/0975045224008

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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