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Nt1330 Unit 1 Math Test Paper

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\noindent Now we will compare the risk measure determined by Corollary \ref{4-cl3} with other risk measures in literature. \begin{remark} \em{ Let $c^{*}_{q}=pF_{X}^{-1}(q)+(1-p)F_{X}^{-1+}(q)$ and $\rho(X)=F_{X}^{-1}(q)$, where $q\in(0,1)$, then $q^{*}=q$. In Corollary \ref{4-cl3}, for given $p\in[0,1]$, if $qc^{*}_{q}$; if $q>\frac{\beta_{1}}{\beta_{1}+\gamma_{2}}$, then $c^{*} \frac{\beta_{1}}{\beta_{1}+\gamma_{2}}$. The order of $c^{**}$ and $c^{*}$ depends on the value of the parameters.} \qed
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