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In this paper, we consider a fairly large class of dependent Sparre Andersen risk models where the claim sizes belong to the class of Coxian distributions. We analyze the Gerber-Shiu discounted penalty function when the penalty function depends on the deficit at ruin. We show that the system of equations needed to solve for this quantity is surprisingly simple. Various applications of this resu...

The Gerber-Shiu function provides a unified framework for the evaluation of variety risk quantities. Ever since its establishment, it has attracted constantly increasing interests in actuarial science, whereas conventional research been focused on finding analytical or semi-analytical solutions, either which is rarely available, except limited classes penalty functions rather simple models. In ...