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Risk aggregation and Extreme Events [60]

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Bullet points include: In practice not very straightforward, usually involves Choosing suitable family or families for marginals (e.g. gamma distribution) And selecting from this family, e.g. using maximum likelihood or (generalised) method of moments Choosing suitable family for copula (e.g. Clayton) And selecting from this family, e.g. again using maximum likelihood or (generalised) method of moments N.B. Max likelihood can be ‘true’, i.e. both steps jointly simultaneously, more commonly is ‘canonical’, i.e. for step (b) is based on observed marginals Deriving pdf/cdf from combination and e.g. computing VaR as value of k for which (I(y) is indicator function, i.e. 1 if y > 0, otherwise 0):

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