The Gerber-Shiu expected discounted penalty function for risk processes with two interests and a constant dividend barrier under absolute ruin

This paper studies the absolute ruin in compound Poisson risk model with two nonnegative interests and a constant dividend barrier.First,an auxiliary function is defined for the Gerber-Shiu expected discounted penalty function.Second,an integro-differential equation for the auxiliary function is derived.Finally,in the case of exponential individual claim,the explicit expressions for the GerberShiu expected discounted penalty function are obtained by the auxiliary function.