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Hofert, Marius; McNeil, Alexander J.

Subadditivity of value-at-risk for Bernoulli random variables. (English) Zbl 1312.91082

Stat. Probab. Lett. 98, 79-88 (2015).
Summary: Necessary and sufficient conditions for the subadditivity of value-at-risk (\(\text{VaR}_\alpha\)) for portfolios of bonds are presented under various dependence assumptions. For sufficiently large \(\alpha\), \(\text{VaR}_\alpha\) is subadditive. However, for any \(\alpha\) one can construct portfolios for which \(\text{VaR}_\alpha\) is superadditive.

MSC:

91G10 Portfolio theory
91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics

Keywords:

risk measure; value-at-risk; superadditivity; Bernoulli random variables; portfolio of bonds

Software:

QRM
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References:

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