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The perturbed compound Poisson risk model with constant interest and a threshold dividend strategy. (English) Zbl 1222.91023

Summary: We consider the compound Poisson risk model perturbed by diffusion with constant interest and a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generation function and the \(n\)th moment of the present value of all dividends until ruin are derived. We also derive integro-differential equations with boundary conditions for the Gerber-Shiu functions. The special case that the claim size distribution is exponential is considered in some detail.

MSC:

91B30 Risk theory, insurance (MSC2010)
91G80 Financial applications of other theories
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