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PROPERTIES OF SECOND-ORDER REGULAR VARIATION AND EXPANSIONS FOR RISK CONCENTRATION

Published online by Cambridge University Press:  30 July 2012

Wenhua Lv ,
Tiantian Mao  and
Taizhong Hu
Wenhua Lv
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026People's Republic of China E-mails: whlzhm@mail.ustc.edu.cn; mttiy@mail.ustc.edu.cn; thu@ustc.edu.cn
Tiantian Mao
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026People's Republic of China E-mails: whlzhm@mail.ustc.edu.cn; mttiy@mail.ustc.edu.cn; thu@ustc.edu.cn
Taizhong Hu
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026People's Republic of China E-mails: whlzhm@mail.ustc.edu.cn; mttiy@mail.ustc.edu.cn; thu@ustc.edu.cn
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Abstract

The purpose of this study is two-fold. First, we investigate further properties of the second-order regular variation (2RV). These properties include the preservation properties of 2RV under the composition operation and the generalized inverse transform, among others. Second, we derive second-order expansions of the tail probabilities of convolutions of non-independent and identically distributed (i.i.d.) heavy-tail random variables, and establish second-order expansions of risk concentration under mild assumptions. The main results extend some ones in the literature from the i.i.d. case to non-i.i.d. case.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 4 , October 2012 , pp. 535 - 559
Copyright
Copyright © Cambridge University Press 2012

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