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Open AccessArticle

On Double Value at Risk

School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
Securities Co., Ltd., Beijing 102627, China
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Risks 2019, 7(1), 31;
Received: 10 February 2019 / Revised: 2 March 2019 / Accepted: 5 March 2019 / Published: 8 March 2019
Value at Risk (VaR) is used to illustrate the maximum potential loss under a given confidence level, and is just a single indicator to evaluate risk ignoring any information about income. The present paper will generalize one-dimensional VaR to two-dimensional VaR with income-risk double indicators. We first construct a double-VaR with ( μ , σ 2 ) (or ( μ , V a R 2 ) ) indicators, and deduce the joint confidence region of ( μ , σ 2 ) (or ( μ , V a R 2 ) ) by virtue of the two-dimensional likelihood ratio method. Finally, an example to cover the empirical analysis of two double-VaR models is stated. View Full-Text
Keywords: double-VaR; joint confidence region; (μ,VaR2) double-VaR; joint confidence region; (μ,VaR2)
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Zhang, W.; Zhang, S.; Zhao, P. On Double Value at Risk. Risks 2019, 7, 31.

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