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

An insurer models the annual losses from its fire and engineering portfolios. It fits a marginal distribution to each line separately and wants to combine them into a joint model without changing either marginal. By Sklar's theorem, what does the copula supply?

The copula supplies the dependence structure linking the marginals. By Sklar's theorem, a joint distribution splits into the marginal distributions and a copula, so the marginals can be fitted separately and then joined through the copula without changing them.

  1. AThe dependence structure linking the two marginal distributionsCorrect
  2. BThe marginal mean of each line of business
  3. CThe tail index of each individual marginal distribution
  4. DThe reinsurance retention for each line
  5. The number of claims in each line

Explanation

Sklar's theorem splits a joint distribution into its marginals and a copula. The copula carries only the dependence between the uniform transforms of the variables. Marginal features such as means and tail indices belong to the marginal distributions, not to the copula.

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