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The Actuary The magazine of the Institute & Faculty of Actuaries

Distributions of infinite variance

I read with interest David Nutting’s comments on distributions with infinite variance (Letters, October 2005). This would imply, for practical models, that the underlying distributions have infinite support with heavy tails. Since actuarial work is focused on modelling financial quantities, there is a bound on the upper – or for that matter – lower support of realisations that can occur. For example, a loss could never exceed the world GDP. Therefore distributions with infinite variance, and by implication, infinite support are unrealistic representations of the risks that we analyse. However, this flaw is also present in finite variance distributions, such as the ubiquitous normal distribution.