2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156339In this paper, we consider the perturbed renewal risk process. Systems of integro-differential equations for the Gerber-Shiu functions at ruin caused by a claim and oscillation are established, respectively. The explicit Laplase transforms of Gerber-Shiu functions are obtained, while the closed form expressions for the Gerber-Shiu functions are derived when the claim amount distribution is from the rational family. Finally, we present numerical examples intended to illustrate the main results.23 pages with 2 figuresProbability60K10; 60G51; 60J55text