Some contributions to mathematical finance and management.

Summary In the first part, we generalize results from the theory of arbitrage to the case of non-linear exchanges. We show the equivalence between two notions of no arbitrage and the existence of consistent price systems, and we consider the over-replication problem. The second part presents two original principles of conditional deviations, derived from financial problems. We give a large deviation approximation of the law of a pair of unobservable processes conditional on an observed function. We also show a conditional large deviations principle for the law of the solution of a couple-dependent SRDE. In the third part, we study the case of a hydroelectric power producer facing two sources of hazards: rainfall and price. We show that the value function of the corresponding optimal control problem is the unique viscosity constrained solution of a nonlinear PDE.