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On a Risk Model with Dependence between Claim Sizes and Claim Intervals under a Linear Dividend Barrier and Stochastic Interest

The risk model with interclaim-dependent claim sizes is studied in the presence of a linear dividend barrier and stochastic interest. An integro-differential equation for some Gerber-Shiu discounted penalty functions is derived. We show that its solution can be expressed as the solution to the Gerber-Shiu discounted penalty function in the same risk model with the absence of a barrier and a combination of two linearly independent solutions to the associated homogeneous integro-differential equation.