Suppose $X_{1}$ and $X_{2}$ are jointly normal positions with parameters $mu_{1}, mu_{2}, sigma_{1}, sigma_{2}, sigma_{12}$. Show that

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Suppose $X_{1}$ and $X_{2}$ are jointly normal positions with parameters $\mu_{1}, \mu_{2}, \sigma_{1}, \sigma_{2}, \sigma_{12}$. Show that

\[\operatorname{VaR}_{h}\left(X_{1}+X_{2}\right) \leq \operatorname{VaR}_{h}\left(X_{1}\right)+\operatorname{VaR}_{h}\left(X_{2}\right) .\]

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Investment Science

ISBN: 9780199740086

2nd Edition

Authors: David G. Luenberger

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