Saturday, April 15, 2017

What is the meaning of subadditivity in a risk measure?


The subadditivity reads:


$\rho(X_1+X_2) \leq \rho(X_1) + \rho(X_2)$


What is the meaning of this condition? I can vaguely accept that one should diversify the investment portfolio. Or, I can understand that $\rho(X_1+X_2)$ describes the situation of two assets $X_1$ and $X_2$ held together. Then what is the meaning of $\rho(X_1) + \rho(X_2)$? One person holds $X_1$ and another person holds $X_2$? I am having difficulty to interpret the right-hand-side.




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