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The Erlang(2) risk model with a two-step premium rate. (English) Zbl 1174.91506

Summary: In this paper, we consider a compound renewal risk process with a two-step premium rate in which the claim waiting times are Erlang(2) distributed. An integro-differential equation with certain boundary condition for the Gerber-Shiu function is derived and solved. By using this result, we obtain the explicit result about the Laplace transform of the time of ruin and ruin probability when the claim sizes are exponentially distributed.

MSC:

91B30 Risk theory, insurance (MSC2010)
60K05 Renewal theory
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