An explicit model of default time with given survival probability

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• 作者：Monique Jeanblanc^a ; ^b ; Shiqi Song^a ; ^{bachsuitepremier@gmail.com"" rel=""nofollow}
• 关键词：Credit risk ; Cox model ; Progressive enlargement of filtrations ; Semimartingale decomposition formula
• 刊名：Stochastic Processes and their Applications
• 出版年：2011
• 出版时间：August 2011
• 年：2011
• 卷：121
• 期：8
• 页码：1678-1704
• 全文大小：356 K

文摘

For a given filtered probability space , an -adapted continuous increasing process Λ and a positive - local martingale N such that Λ₀=0 and N_te^−Λ_t≤1, we construct a probability measure and a random time τ 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.