PHC Procope

PHC Procope
Modeling and simulation of illiquid financial markets

The mathematical study of illiquid financial markets is a current and very important topic for researchers and regulators of these markets. There is a very wide class of subjects around illiquidity. One of them concerns the optimal trade execution. Roughly speaking, the agent wants to close or consolidate her position during a given period and to minimize the expected costs generated by her liquidation strategy. These costs arise from the market impact and transaction costs. To quantify the associated risks, there is a growing interest on stochastic models. And backward stochastic differential equations (BSDEs) is a powerful tool to obtain the optimal execution strategies. 

The first aim of this project is to propose a multidimensional generalization for the optimal liquidation problem. This problem has not been developed until now, but has practical consequences. Indeed the agent may have different positions in her portfolio. And the market frictions are not the same for all assets, which means that we cannot aggregate them and only consider the global portfolio. Moreover these assets may be correlated and we want to characterize how this dependence influences the execution strategies. 

The second goal of the project is to propose and study appropriate efficient numerical methods. In this context existing numerical schemes cannot be directly used, because the mandatory liquidation creates a terminal singularity for the related BSDE (or PDE). Hence the analysis of the algorithms is a challenging problem. Recently mean-field methods have shown remarkable success to solve BSDE, in particular in high-dimensional settings. We will apply the group's expertise on gradient boosting techniques to propose efficient algorithms for optimal liquidation. 

TEAM

French part (Le Mans Université, Laboratoire Manceau de Mathématiques)

M. CACITTI-HOLLAND DORIAN*, PhD student,

M. ESSTAFA YOUSSEF*, Maitre de conférences 

M. POPIER ALEXANDRE*, Professeur des universités, coordinator

German part (University of Wuppertal, Applied and Computational Mathematics)

Mme ACKERMANN JULIA*, Post-Doc position,

M. KLEINBERG KONRAD*, PhD student,

M. KRUSE THOMAS*, Professor, coordinator

The two coordinators of the French and the German team, T. Kruse and A. Popier, have built a considerable history of mutual cooperation during the last ten years that has resulted in various joint publications in internationally renowned academic journals. The project will reinforce and extend this fruitful relationship to further members of the two research groups to ultimately establish a longstanding connection between the Chair of Applied and Computational at the University of Wuppertal and the Laboratoire Manceau de Mathématiques at the University of Le Mans.