Solvability Conditions of Integro-Differential Equation on Classical Risk Models with Exponential Claims via Laplace Transform

Dadang Amir Hamzah (President University)
Ranny Febrianti (President University)

Jurnal Rekayasa Teknologi dan Sains Terapan
Vol 4 No 2 (2023): Jurnal Rekayasa Teknologi dan Sains Terapan Vol. 4 No. 2

In the classical risk models, ruin probability can be determined by solving the initial value problem of the integro-differential equation. This equation is determined by considering the process that arises from the amount of the first claim in a classical risk model. The Laplace transform is applied to solve the integro-differential equation. The parameters that appear in the model such as loading factor, claim amount distribution, and number of claim parameters can influence the successful application of this method, that is for some value of parameters in the model, the Laplace transform can return the analytical solution of the integro differential equation. In this paper, the lower bound of the loading factor is determined. The claims amount distribution is divided into three different forms of exponential functions. The bound will guarantee the successful application of Laplace transforms in solving the integro-differential equation.