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value at risk example - y=x^2 4.5 4 3.5 3 2.5 y 2 1.5 1 0.5...

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-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 y=x^2 x y
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-2 -1.75 -1.5 -1.25 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 0 1 2 3 4 5 6 7 8 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 y = x^2 + z^2 x y z
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x f(x) = x^2 -2 4 x -2 -1.75 -1.5 -1.25 -1.9 3.61 -2 8 7.06 6.25 5.56 -1.8 3.24 -1.75 7.06 6.13 5.31 4.63 -1.7 2.89 -1.5 6.25 5.31 4.5 3.81 -1.6 2.56 -1.25 5.56 4.63 3.81 3.13 -1.5 2.25 -1 5 4.06 3.25 2.56 -1.4 1.96 -0.75 4.56 3.63 2.81 2.13 -1.3 1.69 -0.5 4.25 3.31 2.5 1.81 -1.2 1.44 -0.25 4.06 3.13 2.31 1.63 -1.1 1.21 0 4 3.06 2.25 1.56 -1 1 0.25 4.06 3.13 2.31 1.63 -0.9 0.81 0.5 4.25 3.31 2.5 1.81 -0.8 0.64 0.75 4.56 3.63 2.81 2.13 -0.7 0.49 1 5 4.06 3.25 2.56 -0.6 0.36 1.25 5.56 4.63 3.81 3.13 -0.5 0.25 1.5 6.25 5.31 4.5 3.81 -0.4 0.16 1.75 7.06 6.13 5.31 4.63 -0.3 0.09 2 8 7.06 6.25 5.56 -0.2 0.04 -0.1 0.01 Using the solver to find minimize y = f(x,z) = x^ 0 0 0.1 0.01 x z f(x,z) 0.2 0.04 0 0 0 0.3 0.09 0.4 0.16 Using the solver to find minimize y = f(x,z) = x^ 0.5 0.25 subject to x+z = 1 0.6 0.36 constraint 0.7 0.49 x z x+z f(x,z) 0.8 0.64 0.500 0.500 1.000 0.500 0.9 0.81 1 1 1.1 1.21 1.2 1.44 1.3 1.69 1.4 1.96 1.5 2.25 1.6 2.56 1.7 2.89 1.8 3.24 1.9 3.61 2 4
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z -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 5 4.56 4.25 4.06 4 4.06 4.25 4.56 5 5.56 4.06 3.63 3.31 3.13 3.06 3.13 3.31 3.63 4.06 4.63 3.25 2.81 2.5 2.31 2.25 2.31 2.5 2.81 3.25 3.81 2.56 2.13 1.81 1.63 1.56 1.63 1.81 2.13 2.56 3.13 2 1.56 1.25 1.06 1 1.06 1.25 1.56 2 2.56 1.56 1.13 0.81 0.63 0.56 0.63 0.81 1.13 1.56 2.13 1.25 0.81 0.5 0.31 0.25 0.31 0.5 0.81 1.25 1.81 1.06 0.63 0.31 0.13 0.06 0.13 0.31 0.63 1.06 1.63 1 0.56 0.25 0.06 0 0.06 0.25 0.56 1 1.56 1.06 0.63 0.31 0.13 0.06 0.13 0.31 0.63 1.06 1.63 1.25 0.81 0.5 0.31 0.25 0.31 0.5 0.81 1.25 1.81 1.56 1.13 0.81 0.63 0.56 0.63 0.81 1.13 1.56 2.13 2 1.56 1.25 1.06 1 1.06 1.25 1.56 2 2.56 2.56 2.13 1.81 1.63 1.56 1.63 1.81 2.13 2.56 3.13 3.25 2.81 2.5 2.31 2.25 2.31 2.5 2.81 3.25 3.81 4.06 3.63 3.31 3.13 3.06 3.13 3.31 3.63 4.06 4.63 5 4.56 4.25 4.06 4 4.06 4.25 4.56 5 5.56 ^2 + z^2 ^2 + z^2
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1.5 1.75
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