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October  2009, 5(4): 719-736. doi: 10.3934/jimo.2009.5.719

Random time ruin probability for the renewal risk model with heavy-tailed claims

Yuebao Wang 1, , Qingwu Gao 1, , Kaiyong Wang 1, and  Xijun Liu 2,

1. 

Department of Mathematics, Soochow University, Suzhou, 215006, China, China, China
2. 

Foundation Department, The First Aeronautical College of Air Force, Xinyang, 464000, China

Received  September 2008 Revised  March 2009 Published  August 2009

In this paper, we investigate the asymptotic behavior of the random time ruin probability for the renewal risk model with heavy-tailed claim sizes. Under the assumption that the claim sizes are independent and long-tailed, we give the equivalent conditions on asymptotic behavior for the random time ruin probability, where the independent or dependent structure among the inter-arrival times is not needed. While, under the assumption that the claim sizes are of some negative dependence structure and consistently varying tails, we obtain the sufficient condition of asymptotic behavior for the random time ruin probability which will require some negative dependence structure among the inter-arrival times.
Keywords: Renewal risk model, random time ruin probability, heavy-tailed claims, negative dependence..
Mathematics Subject Classification: Primary: 62P05; Secondary 62E20, 60F1.
Citation: Yuebao Wang, Qingwu Gao, Kaiyong Wang, Xijun Liu. Random time ruin probability for the renewal risk model with heavy-tailed claims. Journal of Industrial and Management Optimization, 2009, 5 (4) : 719-736. doi: 10.3934/jimo.2009.5.719
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