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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Introduction to copulas

Which statement about Archimedean copulas is correct?

Archimedean copulas are constructed from a generator function φ, with C(u,v) equal to the inverse generator applied to φ(u) + φ(v). They need no correlation matrix or normal marginals, and different families show different tail dependence patterns.

  1. AThey are built from a generator function φ, with C(u,v) = φ^(-1)(φ(u) + φ(v))Correct
  2. BThey can only be defined in two dimensions and never extended further
  3. CThey always have the same tail dependence in both tails
  4. DThey are constructed from a correlation matrix only
  5. They require the marginal distributions to be normal

Explanation

An Archimedean copula is defined through a decreasing convex generator φ with φ(1)=0, as C(u,v)=φ^(-1)(φ(u)+φ(v)). Tail behaviour differs by family (Clayton lower, Gumbel upper), and they can be extended to higher dimensions with restrictions. Marginals can be any distributions.

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