Asymptotic results for heavy-tailed distributions using defective renewal equations

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• 作者：Georgios Psarrakos
• 刊名：Statistics and Probability Letters
• 出版年：2009
• 出版时间：15 March 2009
• 年：2009
• 卷：79
• 期：6
• 页码：774-779
• 全文大小：406 K

文摘

In this note, we investigate the asymptotic behavior of two special functions that satisfy defective renewal equations and have a key role in risk theory. Heavy-tailed distributions are important in our analysis. Furthermore, applying our results to the renewal and classical models of risk theory yields a generalisation of a well-known asymptotic formula of [Embrechts, P., Veraverbeke, N., 1982. Estimates for the probability of ruin with special emphasis on the possibility of large claims. Insurance Math. Econom. 1, 55–72].