On a generalized Gerber-Shiu function in a compound Poisson model perturbed by diffusion

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• 作者：Chaolin Liu (1)
  Zhimin Zhang (1)
  
  1. College of Mathematics and Statistics ; Chongqing University ; Chongqing ; China
  
• 关键词：Generalized Gerber ; Shiu function ; integral equations ; Laplace transform ; combination of exponentials
• 刊名：Advances in Difference Equations
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,118 KB
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• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

In the spirit of a publication by Cheung in 2013 we study generalized Gerber-Shiu functions in the compound Poisson risk model perturbed by diffusion. These generalized Gerber-Shiu functions can be used to analyze the moments of the total discounted claim costs until ruin. Integral equations for the generalized Gerber-Shiu functions are derived and a solution procedure is also provided. Some explicit results are given when the claim size density is a combination of exponentials, and some numerical results are also given.