S^(m)在凸序意义下的上下界及其应用  

Upper and lower bounds for S^((m)) in the sense of convex order and their application

作　　者：颜荣芳[1] 周霞[1] 付桐林[2] 

机构地区：[1]西北师范大学数学与信息科学学院,甘肃兰州730070 [2]陇东学院数学系,甘肃庆阳745000

出　　处：《兰州大学学报（自然科学版）》2008年第4期112-117,共6页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金(60474029);甘肃省自然科学基金(ZS-011-A25-024-G);甘肃省教育厅科研项目(041-14);西北师范大学创新工程项目(NWNU-KJCXGC-03-39)资助．

摘　　要：对于m个相互独立的随机向量X_1=(X_(1,1),X_(1,2),…,X_(1,n)),X_2=(X_(2,1),X_(2,2),…,X_(2,n)),…,X_m=(X_(m,1),X_(m,2),…,X_(m,n)),记S^((m))=sum from (i=1) to n X_(1,i)X_(2,i)…X_(m,i).讨论了S^((m))在凸序意义下的上下界,得到了S^((3))上下界的分布函数和停止损失保费;给出了随机年金在凸序意义下的上界,并得到了随机利率下离散随机年金现值的期望.For m independent random vectors X1=（X1,1,X1,2,…,X1,n）,X2=（X2,1,X2,2,…,X2,n）,…,Xm=（Xm,1,Xm,2,…,Xm,n）,let S^（m）=Σni=1X1,iX2,i…Xm,i. The upper and lower i=1 22, n） bounds of S^（m） in the sense of convex order were investigated, and the distribution function and stop-loss premium of the upper and lower bounds of S^（3） were derived; meanwhile, the upper bounds for stochastic annuities in the sense of convex order were obtained and the expectation of present value functions of discrete stochastic annuities under random interest was realized.

关 键 词：年金现值 随机利率 同单调 停止损失序 停止损失保费 

分 类 号：O211.67[理学—概率论与数理统计]