Advanced Approach to Estimate Stopped Sum Geometric Distribution in Insurance System Using Saddle-Point Approximation

In this study, an advanced technique is used to derive the cumulative distribution function approximation for the complex stopped sum Geometric model, which is commonly applied in insurance systems. The study confirms the accuracy of the saddle-point approximation. Numerical calculations, compared with the corresponding normal approximation, are used to demonstrate the superiority of the saddle-point method as an effective solution for approximating these intractable distributions.