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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Compound distributions and their applications in risk modelling

Which statement best describes a benefit of computing the distribution of aggregate claims using the fast Fourier transform (FFT) rather than direct convolution?

The FFT method transforms the discretised severity distribution, applies the probability generating function of the claim number to the transformed values, and inverts the result. This yields the whole aggregate distribution efficiently and does not require the (a,b,0) class.

  1. AIt computes the aggregate distribution efficiently by transforming the severity to the frequency domain, applying the probability generating function of N, and invertingCorrect
  2. BIt gives exact results for continuous severities without any discretisation
  3. CIt requires the claim number distribution to be in the (a,b,0) class
  4. DIt produces only the mean and variance of aggregate claims
  5. It works only when claim amounts are normally distributed

Explanation

FFT discretises the severity, transforms it, applies the PGF of N to the transformed values, then inverts. It works for any N with a known PGF, still requires discretisation, and returns the full distribution, not just moments.

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