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Show that the risk measure based on the standard deviation of the premium
satisfies Axiom S (subadditivity),
T (translation invariance),
and PH (positive homogeneity) ,
but not Axiom M (monotonicity).
Please use formulas
( X ) = X + X ( X + Y ) ( X ) + ( Y ) ( X + a ) = ( X ) + a ( a X ) = a ( X ) ( X ) ( Y )

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Show that the risk measure based on the standard deviation of the prem.pdf

  • 1. Show that the risk measure based on the standard deviation of the premium satisfies Axiom S (subadditivity), T (translation invariance), and PH (positive homogeneity) , but not Axiom M (monotonicity). Please use formulas ( X ) = X + X ( X + Y ) ( X ) + ( Y ) ( X + a ) = ( X ) + a ( a X ) = a ( X ) ( X ) ( Y )