An explicit model of default time with given survival probability

For a given filtered probability space , an -adapted continuous increasing process [Lambda] and a positive - local martingale N such that [Lambda]0=0 and Nte-[Lambda]t<=1, we construct a probability measure and a random time [tau] such that and . The probability is linked with the well-known Cox model by an explicit density function. Various properties exist, which characterize from others. Let with . We establish the (H')-property between the filtrations and , and we provide the enlargement of filtration formula.