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

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• 作者：Shanshan Wang (1)
  Chuangji An (2)
  Chunsheng Zhang (2)
  
  1. Department of Mathematics ; Tianjin Polytechnic University ; Tianjin ; 300387 ; China
  2. School of Mathematical Sciences and LPMC ; Nankai University ; Tianjin ; 300071 ; China
  
• 关键词：Discrete risk model ; Gerber ; Shiu function ; time of ruin ; surplus before ruin ; deficit at ruin ; dividend ; 60J05 ; 91B30
• 刊名：Frontiers of Mathematics in China
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：10
• 期：2
• 页码：377-393
• 全文大小：219 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Higher Education Press, co-published with Springer-Verlag GmbH
• ISSN：1673-3576

文摘

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.