信用リスクとキュムラント母関数

In reading about credit risk, I was perplexed by a metric psi and the use of the expression "cumulant generating function". The cumulant generating function is the log of the moment generating function, it seems.
The article also involves the probability of default of each of m obligors in a portfolio and the default threshold of the portfolio itself. A parameter theta is chosen to correct probabilities in a technique known as "importance sampling" such that the variance of the "estimator". This adjustment technique is known as "exponential twisting".