Gerber-Shiu discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy

Hu Yang and Zhimin Zhang

Insurance: Mathematics and Economics, 2008, vol. 42, issue 3, 984-991

Abstract: This paper studies a Sparre Andersen model in which the inter-claim times are generalized Erlang(n) distributed. We assume that the premium rate is a step function depending on the current surplus level. A piecewise integro-differential equation for the Gerber-Shiu discounted penalty function is derived and solved. Finally, to illustrate the solution procedure, explicit expression for the Laplace transform of the time to ruin is given when the inter-claim times are generalized Erlang(2) distributed and the claim amounts are exponentially distributed.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:42:y:2008:i:3:p:984-991

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