RUIN PROBABILITY IN THE CLASSICAL RISK PROCESS WITH WEIBULL CLAIMS 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 However, when the analytical solution cannot be determined since the Laplace transform is no longer applicable due to the presence of an improper integral that is not possible to solve analytically.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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