Numerical Finance with Backward Stochastic Differential Equations: An Exploration of Three Schemes

The main aims of this research are to study various numerical schemes in the approximation of the occurring expectations and their applications in numerically solving BSDEs. We focus on numerical expectation/finite measure integration since the majority of the BSDE solvers consists of two parts, conditional expectations computations, and deterministic functions to map these expectations to target approximations. By simply changing the approximation for conditional expectations, we can effectively generate various schemes for BSDEs that can suit different requirements. Furthermore, our results carry implications in numerical integration too. In this thesis, we focus on the mathematical properties of these approximations. We will discuss the fundamental assumptions for them, give complete descriptions, derive
error bounds and conduct numerical experiments. The main goal is to analyze these approximations. We will also touch upon the financial applications of BSDEs.