Study of numerical methods for partial hedging and switching problems with costs uncertainty.

Summary In this thesis, we make some contributions to the theoretical and numerical study of some stochastic control problems, as well as their applications to financial mathematics and financial risk management. These applications concern problems of valuation and weak hedging of financial products, as well as regulatory issues. We propose numerical methods to efficiently compute these quantities for which no explicit formula exists. Finally, we study backward stochastic differential equations related to new switching problems with cost uncertainty.