Coupled Mean-field Reflected Forward-backward Stochastic Differential Equations

In this thesis,we mainly study the existence and the uniqueness of the solutions,as well as the comparison theorem for a new type of coupled mean-field reflected forward-backward stochastic differential equations(MFRFBSDEs for short).We also consider the viscosity solutions of the related non-local partial differential equations.Moreover,we study the general mean-field reflected backward stochastic differential equations under the continuity assumptions,that is,the coefficients of the equations both depend on the solutions and their distributions.In more details,the thesis is divided into two parts.In the first part,we consider the following coupled MFRFBSDE:#12Under the continuity assumptions,we use the method of constructing two increasing sequences to approximate respectively the solutions of the equations to prove the exis-tence of the solution for the above equation(0).For the uniqueness of the solution for the equation(0),we give a counter-example to explain that we can not get the uniqueness of the solution only under Lipschitz condition for such coupled equation(0).When the ob-stacle process h(t,Xt)=?(t)+?/?Xt and it satisfies some quasi-monotonicity assumption,we get the uniqueness of the solution of equation(0)and also comparison theorem.Furthermore,we use the contradiction method to give the probabilistic interpretation to the viscosity solution of the following non-local parabolic partial differential equation:#12In the second part,we study the following general mean-field reflected backward stochastic differential equation:#12We prove the existence and the uniqueness of the solution for the above equation under Lipschitz condition and give the comparison theorem for one-dimensional case.Furthermore,we consider the following general coupled MFRFBSDE:#12Under the continuity assumptions,we construct two new monotone sequences to approximate respectively the solutions of the equations to prove the existence of the solution for the above equation(1).In addition,we obtain the uniqueness of the solution and comparison theorem for the equation(1)which the obstacle process h(t,Xt)=?(l)??/?Xt.