信用リスクを計算する方程式

最近フーリエ変換に頼るリスク計算方法に関わる論文を読んでいます。
Credit Risk+ assumes portfolio defaults follow a Poisson distribution, and uses a Fast Fourier Transform to solve for the credit loss probability distribution. The logic connecting the starting Poisson distribution with the loss distribution is unclear.
この論文が二つな確率分布を述べています。 The paper discusses probability distributions for both the number of defaults in a portfolio of loans and bonds and the loss due to default in this portfolio. Interestingly, an unconditional Poisson based on the gamma distribution is used for loss amounts, while the negative binomial distribution is used for number of defaults. This is a case where the variance of the obligors is parametrized (the distribution is strictly Poisson if the variance is constant).
The use of the Fourier Transform seems to be justified by the use of convolution to explain the number of defaults in a portfolio of two obligors (or the expected loss). If there is one default in the portfolio, there is either one default by the first obligor and zero by the second or zero defaults by the first obligor and one by the second. The pdf for the portfolio default count is then
p(x) = SUM(i=0 to x) (p1(i)*p2(x-i))
However, how this convolution model is extended to a portfolio of more than two obligors is unclear (perhaps by convolving the convolution of two obligors's defaults with a third obligor, etc in a recurrent convolution).
The CreditRisk+ (Credit Suisse) model computes the probability distribution of credit losses using polynomials A and B. A(z) = a0z^0+a1z+a2z^2+...+arz^r
B(z) = b0z^0+b1z+b2z^2+...+bsz^s
The A(z) coefficients can be solved for expanding the expression:
A(z)= (p*(alpha)/mu)*(SUM(j=1 to m)(epsilon*z^(vj-1)))
Here p and alpha are written in terms of the mean loss rate and loss variance of the portfolio. Epsilon is the expected loss in the jth band, and vj is the exposure in this band. The examples in the paper (Melchiori, on YieldCurve.com) use discrete, integral exposures like 0,1,2.
The B(z) coefficients can be derived by evaluating this summation:
B(z) = 1-(p/mu)SUM(j=1 to m)(uj*z^vj)
where u is the mean default rate (weighted) for the individual band. For n obligors, the above would need to be generalized, but the formulas above hold for a single obligor.
Once the coefficients are derived, the probability of a loss of size n+1, A(n+1) = (1/(b0*(n+1)))**1ai*A(n-I))-(SUM(j=0 to min(s-1,n-1))b(j+1)*(n-j)*A(n-j)))
Once the probability distribution is obtained, an inverse cumulative distribution function calculation can be performed to obtain the 99% credit value at risk (VaR).
The derivation of why the above polynomials are effective at explaining credit loss probability is unclear.

*1:SUM(i=0 to min(r,n