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## The Asymptotic of Finite Time Ruin Probabilities for Risk Model with Variable Interest Rates

Yu Jinyou1,2 Hu Yijun2 Wei Xiao3(1Guanghua School of Management,Peking University,Beijing,100871)(2School of Mathematics and Statistics,Wuhan University,Hubei,430072)(3School of Insurance and CIAS,Central University of Finance and Economics,Beijing,100081)
Consider a discrete time risk model Un=Un-1+Yn)(1+rn)-Xn,n=1,2,…,where U0=x0 is the initial reserve of an insurance company,rn the interest rates,Yn the total amount of premiums,Xn the total amount of claims and Un the reserve at time n.Under some mild conditions on Yn and rn,we obtain the uniform asymptotics relation for the finite time ruin probabilities ψ(x,N)～sum from k=1 to N(FX((1+r1)…(1+rn)x)) as x→∞,where ψ(x,N)=P min 0≤n≤N Un0|U0=x,N≥1,FX(x) is the tail distribution of X1,and the uniformity is with respect to N≥1.
【Fund】： Supported by the National Natural Science Foundation of China(10671149 10801139);; Key Project of Philosophy and Social Sciences Research of the Ministry of Education(07JZD0010)
【CateGory Index】： F224;F840
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 【References】
 Chinese Journal Full-text Database 2 Hits
 1 Jinghai FENG;Lixin SONG;Linna YI;School of Mathematical Sciences,Dalian University of Technology,Liaoning 116024,P. R. China;;On Finite Time Ruin Probability with Random Interest Rate in a Multi-Risk Model[J];Journal of Mathematical Research with Applications;2014-04 2 LIU Mei-xia(Department of Statistics,Jinan University,Guangzhou 510632,P.R.China);The Research of Ruin Probability for a Poisson-Geometric Process Model of Double Line under Stochastic Interest Rates[J];科学技术与工程;2012-18
 【Co-references】
 Chinese Journal Full-text Database 5 Hits
 1 Cheng Junxiang1 Yang Tingting2(College of Mathematics and Information Science,Henan Polytechnic University,Jiaozuo Henan 454000,P.R.China);Bankrupt Probability for a Poisson-Geometric Risk Model of Double Line with Poisson Process under Stochastic Interest[J];北京电子科技学院学报;2011-02 2 Ming Ruixing School of Mathematics and Information Sciences, Jiangxi Normal University, Nanchang 330022, China School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China He Xiaoxia College of Science, Wuhan University of Science and Technology, Wuhan 430081, China Hu Yijun School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China Liu Juan College of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China;UNIFORM ESTIMATE ON FINITE TIME RUIN PROBABILITIES WITH RANDOM INTEREST RATE[J];Acta Mathematica Scientia;2010-03 3 Yu Jinyou1,2 Hu Yijun2 Wei Xiao3(1Guanghua School of Management,Peking University,Beijing,100871)(2School of Mathematics and Statistics,Wuhan University,Hubei,430072)(3School of Insurance and CIAS,Central University of Finance and Economics,Beijing,100081);The Asymptotic of Finite Time Ruin Probabilities for Risk Model with Variable Interest Rates[J];应用概率统计;2010-01 4 ZHOU Shao-wei(College of Science,Shandong University of Science and Technology,Qingdao 266510,Shandong,China);A double-compound Poisson-Geometric risk model and ruin probability[J];山东大学学报(理学版);2009-12 5 ZHANG Jian-ye 1 , WANG Yong-mao 1 , QIN Gui-xia 1 (1. College of Sciences, Yanshan University, Qinhuangdao, Hebei 066004, China);Risk model construction of unit-linked insurance and its ruin probability by martingale analysis[J];燕山大学学报;2008-06
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