Backward Stochastic Differential Equations under Enlarged Filtrations

We provide solution formulas for (linear and non-linear) jump-diffusion backward stochastic differential equations (BSDEs) under diverse enlarged filtration approaches. We also derive a comparison theorem for BSDEs in an enlarged filtration framework and present several applications of our theoretical results. For example, we study temperature derivatives under weather forecasts modeled by an enlarged filtration BSDE, investigate portfolio selection and hedging for an insider with additional information on future price behavior and solve a particular predictive mean-field BSDE in an enlarged filtration setup