The aim of this thesis is to investigate some solutions to the pricing of contingent claims in incomplete markets. We first consider the stochastic targetintroduced by Soner and Touzi (2002) for the general super-replication problem, and extended by Bouchard, Elie and Touzi (2009) in order to...

This PhD dissertation presents three independent research topics in the field of stochastic target and optimal control problems with applications to financial mathematics. In a first part, we provide a PDE characterization of the super hedging price of an American option of barrier types in a...

This PhD thesis considers the optimal trading problem from the stochastic control approach and consists of four parts. In the first part, we begin with the study of the impacts generated by volumes on the price process. We introduce a structural model in which price movements are due to not only...