Section: New Results

Financial issues modelling

Participants : Aurélien Alfonsi, Céline Labart, Jérôme Lelong, J. Acevedo.

Credit risk modelling

A. Alfonsi, C. Labart and J. lelong are studying loss models called “stochastic local intensity models” that have been proposed in the literature. First, they are interested in proving mathematically that these models are well posed (it exists and has a unique solution). Second, they aim to provide numerical tools to sample such dynamics.

Limit order markets

A. Alfonsi has an active collaboration with A. Schied (Mannheim University) on limit order book models. A. Schied has visited the CERMICS two weeks in February 2011 and one week on December. They are currently studying some type of non-Markovian resilience for the limit-order book for which they are able to get the optimal execution strategy in a closed form. Moreover A. Alfonsi and his PhD student J. Acevedo study impact models for which the limit order book shape evolves along the time.

Control of systemic risk

Participants : Agnès Sulem, J.Ph. Chancelier, Andreea Minca.

We are interested in contagion modeling and systemic risk in financial networks. We aim to contribute in particular to the domain of control of such systems in order to reduce the systemic risk. We model the propagation of distress in financial systems as an epidemic on a random graph in which the nodes represent financial institutions and edges the exposure between them. Cascade dynamics may be reduced to the evolution of a multi-dimensional markov chain that corresponds to a sequential discovery of exposures and determines the size of contagion. We study the optimal intervention strategy by a lender of last resort who wants to minimize the size of contagion under budget constraints.