Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/257869 
Year of Publication: 
2019
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 7 [Issue:] 1 [Article No.:] 31 [Publisher:] MDPI [Place:] Basel [Year:] 2019 [Pages:] 1-22
Publisher: 
MDPI, Basel
Abstract: 
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,VaR 2 ) indicators, and deduce the joint confidence region of (μ,σ 2 ) (or (μ,VaR 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.
Subjects: 
double-VaR
joint confidence region
(m,VaR2)
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
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