Methods for estimating the optimal dividend barrier and the probability of ruin

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• 作者：Hans U. Gerber ; Elias S.W. Shiu ; Nathaniel Smith
• 关键词：Optimal dividend barrier ; Ruin probability ; Lé ; vy processes ; Subordinators ; De Vylder approximations ; Diffusion approximations ; Lundberg function ; Lundberg’ ; s fundamental equation ; Gamma processes
• 刊名：Insurance: Mathematics and Economics
• 出版年：2008
• 出版时间：February 2008
• 年：2008
• 卷：42
• 期：1
• 页码：243-254
• 全文大小：319 K

文摘

In applications of collective risk theory, complete information about the individual claim amount distribution is often not known, but reliable estimates of its first few moments may be available. For such a situation, this paper develops methods for estimating the optimal dividend barrier and the probability of ruin. In particular, two De Vylder approximations are explained, and the first and second order diffusion approximations are examined. For several claim amount distributions, the approximate values are compared numerically with the exact values. The De Vylder and diffusion approximations can be adapted to the more general situation where the aggregate claims process is a Lévy process with nonnegative increments.