SDEs and MFGs towards Machine Learning applications

We present results that span three interconnected domains. Initially, our analysis is centred on Backward Stochastic Differential Equations (BSDEs) featuring time-delayed generators. Subsequently, we direct our interest towards Mean Field Games (MFGs) incorporating absorption aspects, with a focus on the corresponding Master Equation within a confined domain under the imposition of Dirichlet boundary conditions. The investigation culminates in exploring pertinent Machine Learning methodologies applied to financial and economic decision-making processes.