Asymptotic aspects of the Gerber–Shiu function in the renewal risk model using Wiener–Hopf factorization and convolution equivalence
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- 作者：Qihe Tang ; Li Wei
- 关键词：Asymptotics ; Convolution equivalence ; Duality principle ; Gerber– ; Shiu function ; Renewal risk model ; Wiener– ; Hopf factorization
- 刊名：Insurance: Mathematics and Economics
- 出版年：2010
- 出版时间：February 2010
- 年：2010
- 卷：46
- 期：1
- 页码：19-31
- 全文大小：2800 K
文摘
We study the asymptotic behavior of the Gerber–Shiu expected discounted penalty function in the renewal risk model. Under the assumption that the claim-size distribution has a convolution-equivalent density function, which allows both heavy-tailed and light-tailed cases, we establish some asymptotic formulas for the Gerber–Shiu function with a fairly general penalty function. These formulas become completely transparent in the compound Poisson risk model or for certain choices of the penalty function in the renewal risk model. A by-product of this work is an extension of the Wiener–Hopf factorization to include the times of ascending and descending ladders in the continuous-time renewal risk model.