Ӧ�ø���ͳ�� 2011, 27(5) 543-560 DOI:      ISSN: 1001-4268 CN: 31-1256

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The Gerber-Shiu Penalty Functions for a Perturbed Risk Model with Two Classes of Risks and a Threshold Dividend Strategy
Sun Guohong,Zhang Chunsheng,Ji Lanpeng
Tianjin Agricultural College,Nankai University,University of Lausanne
Abstract:

In this paper, we study the perturbed risk
model with two classes of claims and a threshold dividend strategy.
We assume that the two claim counting processes are, respectively,
Poisson and renewal process with generalized Erlang(2) inter-claim
times. Integro-differential equations and certain boundary
conditions satisfied by the Gerber-Shiu penalty functions are
derived in terms of matrices. Finally, we show that the closed form
for the Gerber-Shiu penalty functions can be expressed by the
Gerber-Shiu penalty functions without dividend payments and the
matrix composed of two linearly independent solutions to the
corresponding homogeneous integro-differential equations.

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