Risk aggregation and Extreme Events [82]

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Bullet points include: PCA adopts an importance criterion (when identifying each consecutive component) that focuses on contribution to variance, i.e. ‘noise’ What if we use a different importance criterion, that also includes ‘fat-tailed-ness’? E.g. maximise sigma (1+cK), where K is the kurtosis, sigma the tracking error (standard deviation) and c is some constant that represents a trade-off between concentrating on maximising variance and concentrating on maximising kurtosis (if c = 0 then equivalent to PCA) Akin to Cornish-Fisher 4th moment approach to estimating quantiles of a Non-Normal distribution (with zero skew), e.g. 99.5%ile, x = N -1(0.995) = - 2.576 and c = 0.39

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