  The Gerber-Shiu function is a classical research topic in actuarial
science.However, exact solutions are only available in the literature for very
specific cases where the claim amounts follow distributions such as the
exponential distribution. This presents a longstanding challenge, particularly
from a computational perspective. For the classical risk process in continuous
time, the Gerber-Shiu discounted penalty function satisfies a class of Volterra
integral equations. In this paper, we use the collocation method to compute the
Gerber-Shiu function for risk model with interest. Our methodology demonstrates
that the function can be expressed as a linear algebraic system, which is
straightforward to implement. One major advantage of our approach is that it
does not require any specific distributional assumptions on the claim amounts,
except for mild differentiability and continuity conditions that can be easily
verified. We also examine the convergence orders of the collocation method.
Finally, we present several numerical examples to illustrate the desirable
performance of our proposed method.
