Enlargement of filtrations

Carthaginian Enlargement of Filtrations ∗ . †

In this work, we revisit some well-known results in the theory of initial and progressive enlargement of a reference filtration F with a random time τ , providing, under an equivalence assumption slightly stronger than the absolute continuity assumption of Jacod, alternative proofs to the already existing ones. We also characterize martingales in the enlarged filtrations in terms of martingales...

Progressive enlargement of filtrations and Backward SDEs with jumps

This work deals with backward stochastic differential equation (BSDE) with random marked jumps, and their applications to default risk. We show that these BSDEs are linked with Brownian BSDEs through the decomposition of processes with respect to the progressive enlargement of filtrations. We prove that the equations have solutions if the associated Brownian BSDEs have solutions. We also provid...

Stochastic control under progressive enlargement of filtrations and applications to multiple defaults risk management

We formulate and investigate a general stochastic control problem under a progressive enlargement of filtration. The global information is enlarged from a reference filtration and the knowledge of multiple random times together with associated marks when they occur. By working under a density hypothesis on the conditional joint distribution of the random times and marks, we prove a decompositio...

Enlargements of Filtrations

Slope Filtrations

Many slope filtrations occur in algebraic geometry, asymptotic analysis, ramification theory, p-adic theories, geometry of numbers... These functorial filtrations, which are indexed by rational (or sometimes real) numbers, have a lot of common properties. We propose a unified abstract treatment of slope filtrations, and survey how new ties between different domains have been woven by dint of de...