Skip to content

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

A reinsurer uses the Fréchet–Hoeffding bounds to assess aggregate risk on two lines. Which statement about the comonotonic copula M(u,v)=min(u,v) is correct?

The comonotonic copula min(u,v) is the upper Fréchet–Hoeffding bound for all copulas and represents perfect positive dependence. It maximises the joint probabilities, and the lower bound max(u+v−1,0) corresponds to perfect negative dependence. Independence is the product copula uv.

  1. AIt gives the upper bound for any copula and represents perfect positive dependenceCorrect
  2. BIt gives the lower bound for any copula and represents perfect negative dependence
  3. CIt equals the product uv and represents independence
  4. DIt has no tail dependence
  5. It is the Gaussian copula with ρ = 0

Explanation

Every copula satisfies max(u+v−1,0) ≤ C(u,v) ≤ min(u,v). The upper bound min(u,v) corresponds to perfect positive dependence. The lower bound is countermonotonic, and the product copula is independence.

Did you get it right without looking?

One question tells you little. A timed set on Introduction to copulas shows your real accuracy, how long you take and where you lose marks.

Practise Introduction to copulasFree diagnostic mock

More Introduction to copulas questions