Correlation, co-dependency and risk aggregation [29]

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Bullet points include: If X1 and X2 are continuous random variables and C(u1,u2) is their copula then the coefficient of lower tail dependence is: If lambda L > 0, i.e. in (0,1] then X1 and X2 are said to have lower tail dependence. If lambda L = 0 then X1 and X2 are said to be (lower tail) asymptotically independent. Gaussian random variables have zero tail dependence (unless they are perfectly correlated). N.B. Care needed when extrapolating (and hence EVT), as e.g. lambda L may not exist

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