Gerber-Shiu function of a discrete risk model with and without a constant dividend barrier

被引:0
作者
Wang, Shanshan [1 ]
An, Chuangji [2 ,3 ]
Zhang, Chunsheng [2 ,3 ]
机构
[1] Tianjin Polytech Univ, Dept Math, Tianjin 300387, Peoples R China
[2] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China
[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China
基金
中国国家自然科学基金;
关键词
Discrete risk model; Gerber-Shiu function; time of ruin; surplus before ruin; deficit at ruin; dividend; PROBABILITIES;
D O I
10.1007/s11464-014-0409-z
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider the discrete risk model with exponential claim sizes. We derive the finite explicit elementary expression for the joint density function of three characteristics: the time of ruin, the surplus immediately before ruin, and the deficit at ruin. By using the explicit joint density function, we give a concise expression for the Gerber-Shiu function with no dividends. Finally, we obtain an integral equation for the Gerber-Shiu function under the barrier dividend strategy. The solution can be expressed as a combination of the Gerber-Shiu function without dividends and the solution of the corresponding homogeneous integral equation. This latter function is given clearly by means of the Gerber-Shiu function without dividends.
引用
收藏
页码:377 / 393
页数:17
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