Upper and lower bounds for sums of random variables

被引：120

作者：

Kaas, R

Dhaene, J

Goovaerts, MJ

机构：

[1] Univ Amsterdam, Inst Actuarial Sci, NL-1018 WB Amsterdam, Netherlands

[2] Katholieke Univ Leuven, CRIR, Louvain, Belgium

来源：

INSURANCE MATHEMATICS & ECONOMICS | 2000年 / 27卷 / 02期

关键词：

dependent risks; comonotonicity; convex order; cash-flows; present values; stochastic annuities;

D O I：

10.1016/S0167-6687(00)00060-3

中图分类号：

F [经济];

学科分类号：

02 ;

摘要：

In this contribution, the upper bounds for sums of dependent random variables X-1 + X-2 + ... + X-n derived by using comonotonicity are sharpened for the case when there exists a random variable Z such that the distribution functions of the X-i, given Z = z, are known. By a similar technique, lower bounds are derived. A numerical application for the case of lognormal random variables is given. (C) 2000 Elsevier Science B.V. All rights reserved.

引用

页码：151 / 168

页数：18

共 17 条

[1] B├a┬nuerle N., 1998, ASTIN BULL, V28, P59, DOI 10.2143/AST.28.1.519079
[2] A reexamination of the relationship between preferences and moment orderings by rational risk-averse investors
Brockett, PL
Garven, JR
[J]. GENEVA PAPERS ON RISK AND INSURANCE THEORY, 1998, 23 (02): : 127 - 137
[3] Extremal generators and extremal distributions for the continuous s-convex stochastic orderings
Denuit, M
De Vylder, E
Lefèvre, C
[J]. INSURANCE MATHEMATICS & ECONOMICS, 1999, 24 (03) : 201 - 217
[4] The safest dependence structure among risks
Dhaene, J
Denuit, M
[J]. INSURANCE MATHEMATICS & ECONOMICS, 1999, 25 (01) : 11 - 21
[5] On the dependency of risks in the individual life model
Dhaene, J
Goovaerts, MJ
[J]. INSURANCE MATHEMATICS & ECONOMICS, 1997, 19 (03) : 243 - 253
[6] Dhaene J., 1996, ASTIN BULL, V26, P201, DOI DOI 10.2143/AST.26.2.563219
[7] On the distribution of IBNR reserves
Goovaerts, M
Redant, H
[J]. INSURANCE MATHEMATICS & ECONOMICS, 1999, 25 (01) : 1 - 9
[8] GOOVAERTS MJ, 2000, J RISK INSURANCE THE, P1
[9] KAAS R, 1994, ORDERING ACTUARIAL R, P144
[10] KAAS R, 1994, INSUR MATH ECON, V13, P241

← 1 2 →