EDSR and EDSPR with filtration magnification, information asymmetry and hedging problems in financial markets.

Summary The objective of this thesis is to study the existence and uniqueness of solution of backward stochastic differential equations with filtration magnification. The motivation for this mathematical problem comes from the solution of a financial hedging problem by an agent with unknown additional market information. In a first part, we solve this problem, successively in a continuous framework and then with jumps, and show that under the assumption (H3) of the filtration magnification, thanks to a representation theorem of martingales, the RHSD in the coarse space under standard assumptions has a unique solution. One of the main consequences is that, in a complete market, the possession of additional information by the insider does not give him a different hedging strategy. In a second part, we develop a model of an informed and influential agent, which leads us to solve a backward stepwise stochastic differential equation with filtration magnification, and we also obtain an existence and uniqueness theorem for the solution. We also study the incomplete market hedging problem, since due to the influence, the market without information becomes incomplete. Finally, in the last part, we generalize the existence and uniqueness results of the solution of EDSR with filtration magnification to EDSR with random horizon.