From the financial point of view, the purpose of this project is to take into consideration liquidity market frictions and risk management constraints in hedging and optimal allocation problems. From the mathematical point of view, this requires new research in statistics for random processes, theoretical mathematical finance, singular constrained stochastic control policies, highly non linear second order parabolic PDEs, regularity and discrete time approximation of Backward Stochastic Differential Equations (BSDEs). The project is divided in three main tasks, concerning respectively the design of optimal hedging policies under liquidity frictions, the characterization of optimal allocation strategies under risk constraints and finally the corresponding BSDE representation and numerical approximation.

All these problems will be discussed from the mathematical point of view in the most general possible framework and the combination of the whole program will be done on specific problems of interest in practical finance.