Backward stochastic differential equation (BSDE) is a generalization of martingale representation theorem  and it has been widely used for financial derivative pricing and stochastic optimization. Traditionally, most of well-posedness result of BSDE were based on contraction mapping theorem on the space of stochastic processes.
In our work, we were able to transform BSDEs into fixed point problems in the space of Lp random variables. The simplicity of our framework enables us to apply various kind of fixed point theorems which have not been tried in previous literature. In particular, this enables to remove infinite dimensionality arise from time and we were able to use white noise analysis to use topological fixed point theorems. As a result, we were able to generalize previous well-posedness results: e.g. time-delayed type, mean-field type, multidimensional super-linear type.
The talk is aimed for those who are not familiar with BSDE and it is based on BSE's, BSDE's and fixed point theorem (joint work with Patrick Cheridito)