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This paper constructs a Sparre Andersen risk model with a constant dividend barrier in which the claim interarrival distribution is a mixture of an exponential distribution and an Erlang(n) distribution. We derive the integro-differential equation satisfied by the Gerber-Shiu discounted penalty function of this risk model. Finally, we provide a numerical example.

The Gerber-Shiu Discounted Penalty Function of Sparre Andersen Risk Model with a Constant Dividend Barrier