Uniform tail asymptotics for the aggregate claims with stochastic discount in the renewal risk models  

作　　者：ZHU ChunHua GAO QiBing LIN JinGuan 

机构地区：[1]School of Mathematics and Statistics, Nanjing Audit University [2]School of Mathematical Science, Nanjing Normal University [3]Department of Mathematics, Southeast University

出　　处：《Science China Mathematics》2015年第5期1079-1090,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11171001,11271193 and 11171065);Planning Foundation of Humanities and Social Sciences of Chinese Ministry of Education(Grant Nos.11YJA910004 and 12YJCZH128);Natural Science Foundation of the Jiangsu Higher Education Institutions of China(Grant No.13KJD110004)

摘　　要：Considering an insurer who is allowed to make risk-free and risky investments, as in Tang et al.(2010), the price process of the investment portfolio is described as a geometric L′evy process. We study the tail probability of the stochastic present value of future aggregate claims. When the claim-size distribution is of extended regular variation, we obtain an asymptotically equivalent formula which holds uniformly for all time horizons, and furthermore, the same asymptotic formula holds for the finite-time ruin probabilities. The results extend the works of Tang et al.(2010).Considering an insurer who is allowed to make risk-free and risky investments, as in Tang et al. （2010）, the price process of the investment portfolio is described as a geometric Levy process. We study the tail probability of the stochastic present value of future aggregate claims. When the claim-size distribution is of extended regular variation, we obtain an asymptotically equivalent formula which holds uniformly for all time horizons, and furthermore, the same asymptotic formula holds for the finite-time ruin probabilities. The results extend the works of Tang et al. （2010）.

关 键 词：renewal risk models ASYMPTOTICS Levy process UNIFORMITY extended regular variation 

分 类 号：F224[经济管理—国民经济] F830.91