Saturday, April 15, 2017

What is the meaning of subadditivity in a risk measure?


The subadditivity reads:


ρ(X1+X2)ρ(X1)+ρ(X2)


What is the meaning of this condition? I can vaguely accept that one should diversify the investment portfolio. Or, I can understand that ρ(X1+X2) describes the situation of two assets X1 and X2 held together. Then what is the meaning of ρ(X1)+ρ(X2)? One person holds X1 and another person holds X2? I am having difficulty to interpret the right-hand-side.




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