

Indemnity and ALAE distributions  
Indemnity  ALAE  
Parameters  Parameters  
Num L2  Policy Limit  
Unit  Effective ALAE Limit  
Reinsurance  Correlation  
Layer  Copula  
Attachment  Tau  
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Click compute to see results... 
It is interesting to compare the approximation to the actual sum for different copula relationships between the marginals. The Clayton copula (used by default), is pinched towards the origin: correlation is stronger for smaller values of the marginals (see Example 11). Comparing the actual sum of the marginals with the copula vs. the "add noise" approximation, shows that the Clayton slightly thicker in the left tail and thinner in the right tail, as one would expect.
The Gumbel copula is almost the exact opposite of the Clayton: it exhibits closest correlation for larger values of the marginals. Again, looking closely, you can see that the actual sum is thicker in the right tails than the approximation, driven by the shape of the copula.
This example highlights that knowing the marginals and correlation coefficient is not enough to determine the bivariate distribution; it is not even enough to determine the distribution of the sum of the marginals!
To display the desired behaviour, the example uses marginal distributions which are more like aggregate distributions for a whole book than severity distributions; they are too symmetric for a severity distribution.