Next Article in Journal
A Genetic Algorithm for Investment–Consumption Optimization with Value-at-Risk Constraint and Information-Processing Cost
Previous Article in Journal
Model-Free Stochastic Collocation for an Arbitrage-Free Implied Volatility, Part II
Article Menu

Export Article

Open AccessArticle
Risks 2019, 7(1), 31;

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.
Received: 10 February 2019 / Revised: 2 March 2019 / Accepted: 5 March 2019 / Published: 8 March 2019
Full-Text   |   PDF [1213 KB, uploaded 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)

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Zhang, W.; Zhang, S.; Zhao, P. On Double Value at Risk. Risks 2019, 7, 31.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Risks EISSN 2227-9091 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top