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SET-VALUED CASH SUB-ADDITIVE RISK MEASURES

Published online by Cambridge University Press:  11 April 2018

Fei Sun  and
Yijun Hu
Fei Sun
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, People's Republic of China E-mails: sunfei@whu.edu.cn; yjhu.math@whu.edu.cn
Yijun Hu
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, People's Republic of China E-mails: sunfei@whu.edu.cn; yjhu.math@whu.edu.cn
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Abstract

In this paper, we introduce a new class of set-valued risk measures which satisfies cash sub-additivity. Dual representation for them is provided. Moreover, we also investigate dynamic set-valued cash sub-additive risk measures and discuss the corresponding multi-portfolio time consistency. The equivalent characterization of the multi-portfolio time consistency is given. Finally, an example is also given to illustrate the introduction of set-valued cash sub-additive risk measures. The present paper can be considered as a set-valued extension of scalar cash sub-additive risk measures introduced by El Karouii and Ravanelli [8].

Keywords

cash additivecash sub-additivedynamicrisk measureset-valued
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 2 , April 2019 , pp. 241 - 257
Copyright
Copyright © Cambridge University Press 2018 

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