Enlargements of Filtrations and Applications

Enlargements of Filtrations and Path Decompositions at Non Stopping Times

Azéma associated with an honest time L the supermartingale $Z_{t}^{L}=\mathbb{P}[L>t|\mathcal{F}_{t}]$ and established some of its important properties. This supermartingale plays a central role in the general theory of stochastic processes and in particular in the theory of progressive enlargements of filtrations. In this paper, we shall give an additive characterization for these supermarting...

Enlargements of Filtrations

Doob’s Maximal Identity, Multiplicative Decompositions and Enlargements of Filtrations

In the theory of progressive enlargements of filtrations, the supermartingale Zt = P (g > t | Ft) associated with an honest time g, and its additive (Doob-Meyer) decomposition, play an essential role. In this paper, we propose an alternative approach, using a multiplicative representation for the supermartingale Zt, based on Doob’s maximal identity. We thus give new examples of progressive enla...

Progressive Enlargements of Filtrations and Semimartingale Decompositions

We deal with decompositions of F-martingales with respect to the progressively enlarged filtration G and we extend there several related results from the existing literature. Results on G-semimartingale decompositions of F-local martingales are crucial for applications in financial mathematics, especially in the context of modeling credit risk, where τ represents the moment of occurrence of som...

Default times, no-arbitrage conditions and changes of probability measures

In this paper we give a financial justification, based on non arbitrage conditions, of the (H) hypothesis in default time modelling. We also show how the (H) hypothesis is affected by an equivalent change of probability measure. The main technique used here is the theory of progressive enlargements of filtrations.