Ӧ�ø���ͳ�� 2015, 31(3) 277-288 DOI:      ISSN: 1001-4268 CN: 31-1256

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�ؼ����� �����Ʋ�ʱ��   Gerber-Shiu������   �������   ��΢��   ��������.  
Differentiability and Asymptotic Properties of Gerber-Shiu Function Associated with Absolute Ruin Time for a Risk Model with Random Premium Income
Xu Lin, Zhang Liming, Wu Liyuan
School of Mathematics and Computer Sciences, Anhui Normal University

In this paper, the differentiability and asymptotic properties of
Gerber-Shiu expected discounted penalty function (Gerber-Shiu function for short) associated
with the absolute ruin time are investigated, where the risk model is given by classical risk
model with additional random premium incomes. The additional random premium income process is
specified by a compound Poisson process. A couple of integro-differential equations satisfied
by Gerber-Shiu function are derived, several sufficient conditions which guarantee the
second-order or third-order differentiability of Gerber-Shiu function are provided. Based
on the differentiability results, when the individual claim and premium income are both
exponential distribution, the previous integro-differential equations can be deduced into
a third-order constant ordinary differential equation (ODE for short). With the standard
techniques on ODE, we find the asymptotic behavior of absolute ruin probability when the
initial surplus tends to infinity.

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