On asymptotic equivalence among the solutions of some defective renewal equations

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• 作者：Qingwu Gao (1)
  Yu Liu (2)
  Georgios Psarrakos (3)
  Yuebao Wang (2)
  
• 关键词：60F15 ; 62G20 ; 60K05 ; defective renewal equation ; asymptotically equivalent relation ; compound geometric distribution ; renewal risk model ; ruin probability
• 刊名：Lithuanian Mathematical Journal
• 出版年：2013
• 出版时间：October 2013
• 年：2013
• 卷：53
• 期：4
• 页码：391-405
• 全文大小：
• 作者单位：Qingwu Gao (1)
  Yu Liu (2)
  Georgios Psarrakos (3)
  Yuebao Wang (2)
  
  1. School of Mathematics and Statistics, Nanjing Audit University, Nanjing, 211815, PR China
  2. School of Mathematics, Soochow University, Suzhou, 215006, PR China
  3. Department of Statistics and Insurance Science, University of Piraeus, Piraeus, 18534, Greece
  
• ISSN：1573-8825

文摘

We obtain some sufficient conditions for mutually asymptotic equivalence among solutions of some defective renewal equations, where the related distributions can be heavy-tailed but are not required to be subexponential. Particularly, the paper make clearer the asymptotically equivalent relations between the ruin probability and the function introduced by Gerber et al. [H.U. Gerber, M.J. Goovaerts, and R. Kaas, On the probability and severity of ruin, Astin Bull., 17:151–163, 1987] for the standard renewal risk model. The results we obtain modify, improve, and extend some existing results.