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I though about this one more time: method of moments means that you do the following: calculate some statistics (i.e. the moments) on the sample express the moments of the distribution that you want to fit in terms of the parameters of this distribution solve the resulting system of equations. If you estimate $E[S^n]$ by averaging the ...


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as you post 3 questions on this topic and after reading them: this is homerwork/study material- right? So for comparing Fast Fourier, MC and Panjer there are tons of publications out there. For the formulas for the momemts of $S$ look here or google "moments in the collective risk model". You should notice that: If you know the distribution of $N$ and $X$ ...


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You can do the following: For each $i$ in $1$ to number of Mont-Carlo runs $K$ simulate the number of losses $N_i$ simulate $N_i$ many loss-sizes $X_{i,1},\ldots,X_{i,N_i}$ calculate $L_i = \sum_{j=1}^{N_i} X_{i,j}$ Doing this you get a sample of losses $L_1,\ldots,L_K$ and you can do all sorts of hisograms, density fits, VaR, ES calculations on it. ...


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We set out a general scheme for doing this sort of thing in our paper http://ssrn.com/abstract=1401094 and its sequel http://ssrn.com/abstract=1437847 Whilst the case studied is different, the techniques are the same. I also discuss in detail the whole process in a chapter of More Mathematical Finance. The adjoint method when it applies is generally ...



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