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...

The preservation of the semi-martingale property in progressive enlargement of filtrations has been studied by many authors. Most of them focus on progressive enlargement with a honest time, allowing for semi-martingale invariance and simple decomposition formulas. However, times allowing for...

We present a general model for default times, making precise the role of the intensity process, and showing that this process allows for a knowledge of the conditional distribution of the default only "before the default". This lack of information is crucial while working in a multi-default...

Given a filtered probability space , an -adapted continuous increasing process [Lambda] and a positive local martingale N such that satisfies Zt<=1,t>=0, we construct probability measures and a random time [tau] on an extension of , such that the survival probability of [tau], i.e., is equal to Zt for...</=1,t>

We consider a general class of continuous asset price models where the drift and the volatility functions, as well as the driving Brownian motions, change at a random time τ. Under minimal assumptions on the random time and on the driving Brownian motions, we study the behavior of the model in...