A further study on correlation order
Tóm tắt
Let (X1,X2,…,Xn) and (Y1,Y2,…,Yn) be real random vectors with the same marginal distributions, if (X1,X2,…,Xn)≤
c
(Y1,Y2,…,Yn, it is showed in this paper that Σ
=1
X
i≤
cx
Σ
Yi and max1≤k≤n
Σ
X
i≤
icx
max 1≤k≤n
Σ
Yi hold. Based on this fact, a more general comparison theorem is obtained.
Tài liệu tham khảo
Dhaene J, Goovaerts M J. Dependency of risks and stop-loss order, ASTIN Bulletin, 1996, 26: 201–212.
Dhaene J, Wang S, Young V, et al. Comonotonicity and maximal stop-loss premiums, Bulletin of the Swiss Association of Actuaries, 2000(2):99–113.
Joag-Dev J, Proschan F. Negative association of random variables with applications, Ann Statist, 1983, 11: 268–295.
Kaas R, Dhaene J, Vyncke D, et al. A simple geometric proof that comonotonic risks have the convexlargest sum, ASTIN Bulletin, 2002, 32: 71–80.
Lu Tongyu, Zhang Yi. Generalized correlation order and stop-loss order, Insurance: Mathematics and Economics, 2004, 35: 69–76.
Müller A, Stoyan D. Comparison Methods for Stochastic Models and Risks, Willey Series in Probability and Statistics, England: John Wiley & Sons Ltd, 2002.
Shao Q M. Comparison theorem on moments inequalities between negatively associated and independent random variables, Journal of Theoretical Probability, 2000, 13: 343–356.