Ӧ�ø���ͳ�� 2008, 24(3) 319-326 DOI:      ISSN: 1001-4268 CN: 31-1256

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ժҪ�� �����о�������ѷ���ģ�������Ʋ�ʱ����ص�ƽ�����ַ�����. �뾭���Cram\'{e}r-Lundbergģ���������ı��ѹ��̲�����ʱ������Ժ���, ����һ������������ĸ���Possion����. ���ǵõ��˷�����������Ļ��ַ���, ���ṩ��һ���о��Ʋ�����ͳһ����. ���øû��ַ������ǵõ����Ʋ�ʱ��, �Ʋ�ʱ����, �Ʋ�ǰ˲ʱӯ���Laplace�任; ����ָ���ֲ��������������������ǵ��������ʽ, �ƹ���Boikov (2003)�Ľ���.
�ؼ����� �������   ���ַ���   ������   �Ʋ�ʱ��   �Ʋ�ʱ����   �Ʋ�ǰ˲ʱӯ��.  
On the Expected Discounted Penalty Function Associated with the Time of Ruin for a Risk Model with Random Income
Yao Dingjun, Wang Rongming, Xu Lin
School of Finance and Statistics, East China Normal University; School of Mathematic and Computer Science, Anhui Normal University
Abstract: This paper studies the expected discounted penalty function associated with the time of ruin for a risk model with stochastic premium. The premium process is no longer a linear function of time in contrast with the classical Cram\'{e}r-Lundberg model. The aggregate premiums constitute a compound Poisson process which is also independent of the claim process. Integral equation for the penalty function is derived, which provides a unified treatment to the ruin quantities. Applications of the integral equation are given to the Laplace transform of the time of ruin, the deficit at ruin, the surplus immediately before ruin occurs. In some special cases with exponential distributions, closed form expressions for these quantities are obtained, which generalize some known results about the problems of ruin in Boikov (2003).
Keywords: Stochastic premium   integral equation   penalty function   the time of ruin   the deficit at ruin   the surplus immediately before ruin occurs.  
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