クレジット・デフォルト・スワップの値

最近ブリゴ氏とアルフォンセィの論文
を読んでいるけどよく分からない。the author's discuss a Poisson process for defaults and then bring up a variable "uppercase gamma", which seems to represent the number of defaults up to t. However, exp(-(G(u)-G(t))) seems to be used as both the probability and discount factor, and accounts for cases where the default time tai occurs after u.