Ӧ�ø���ͳ�� 2011, 27(3) 256-264 DOI:      ISSN: 1001-4268 CN: 31-1256

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���Ŀ���������ʱ����Ϊ����Erlang($n$)�ֲ��Ĵ����Ÿ���(Sparre
Andersen)���չ���. ���õķ���������Albrecher, et al.\,(2005),
��������Erlang($n$)��������ֽ��$n$��������ָ����������ĺ�.
�������Ʋ�ǰ���ӯ��������Ļ���--΢�ַ���,
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The Maximum Surplus before Ruin in a Generalized
Erlang(n) Risk Process Perturbed by Diffusion
Jiang Wuyuan,Liu Zaiming
Hunan Institute of Science and Technology,Central South University
Abstract:

In this paper, we discuss a renewal risk process
(Sparre Andersen risk model) perturbed by diffusion in which the
claim inter-arrival times are generalized Erlang$(n)$ distributed.
The approach used is similar to that of Albrecher, et al.\,(2005),
decomposing a generalized Erlang$(n)$ random variable into an
independent sum of $n$ exponential random variables.
Integro-differential equations with certain boundary conditions for
the distribution of the maximum surplus before ruin are obtained.
The special case where the claim size distribution is a $K_m$
distribution is considered.

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