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Risk aggregation and Extreme Events [56]

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Bullet points include: With some copulas a similar approach can be used as for Gaussian copula But for others, e.g. Clayton, a different approach is required Suppose we have a pair of uniform random numbers u1 and u2 with a copula C(u1, u2) then: Hence given a pair of independent uniforms, u1 and u2, we may generate a pair of uniforms with joint distribution equal to the copula, u1* and u2* as follows, where C-1(u2|u1) is the inverse of C(u2|u1) with respect to its first argument, u2 Relatively easy if derivatives of copula are simple to calculate analytically

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