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Computing And Approximation Methods For The Distribution Of Multivariate Aggregate Claims, Tao Jin

Electronic Thesis and Dissertation Repository

Insurance companies typically face multiple sources (types) of claims. Therefore, modeling dependencies among different types of risks is extremely important for evaluating the aggregate claims of an insurer. In the first part of this thesis, we consider three classes of bivariate counting distributions and the corresponding compound distributions introduced in a 1996 paper by Hesselager. We implement the recursive methods for computing the joint probability functions derived by Hesselager and then compare the results with those obtained from fast Fourier transform (FFT) methods. In applying the FFT methods, we extend the concept of exponential tilting for univariate FFT proposed by …