Some contributions to financial market modelling with transaction costs

This thesis deals with different problems related to markets with transaction costs and is composed of four parts.In part I, we begin with the study of assymptotic hedging a European option in a local volatility model with bid-ask spread.In part II, we study the optimal consumption problem in a Kabanov model with jumps and with default risk allowed.In part III, we sugest a general market model defined by a liquidation procès. This model is more general than the models with both fixed and proportional transaction costs. We study the problem of super-hedging an option, and the arbitrage theory in this model.In the last part, we study the utility maximization problem under expected risk constraint.