Fast Fourier transform techniques applied to collective risk problems

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Lin, Gary H.
Beekman, John A.
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Thesis (M.S.)
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This thesis is concerned with utilizing new mathematical techniques developed in Sweden for inverting characteristic functions of probability distributions of functionals defined on the collective risk stochastic process. A characteristic function is a Fourier transform. However, such transforms-could not be inverted. With the advent of the electronic computer, the Fast Fourier Transform technique was developed for inverting Fourier Transforms. Essentially these techniques replace integrals over an uncountable number of points by series over a discrete set of points. This thesis will convert some Swedish results into useful forms for American students. It will be concerned with the probability distribution of aggregate claims in a fixed time, as well as ruin probabilities. The thesis will illustrate the basic mathematical techniques with several practical problems. Computer programs and numerical examples will be included.