Efficient Numerical Computation of the Integral Equation for the Ruin Probability

Efficient method of the numerical computation of integral equations is introduced. The equation describes the behavior of the ruin/survival probability under the Cramer-Lundberg model, and the range of integration is possibly infinite. Transforming the infinite interval into a finite interval, we apply the Chebyshev-Gauss-Radau collocation method. Numerical experiments exhibit satisfactory outcomes. Limiting behavior is also treated numerically.