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The Gerber-Shiu function is a classical research topic in actuarialscience.However, exact solutions are only available in the literature for veryspecific cases where the claim amounts follow distributions such as theexponential distribution. This presents a longstanding challenge, particularlyfrom a computational perspective. For the classical risk process in continuoustime, the Gerber-Shiu discounted penalty function satisfies a class of Volterraintegral equations. In this paper, we use the collocation method to compute theGerber-Shiu function for risk model with interest. Our methodology demonstratesthat the function can be expressed as a linear algebraic system, which isstraightforward to implement. One major advantage of our approach is that itdoes not require any specific distributional assumptions on the claim amounts,except for mild differentiability and continuity conditions that can be easilyverified. We also examine the convergence orders of the collocation method.Finally, we present several numerical examples to illustrate the desirableperformance of our proposed method.

Computing Gerber-Shiu function in the classical risk model with interest using collocation method