Robust Operator Learning to Solve PDE

A model solving a family of partial differential equations (PDEs) with a single training is proposed. Re-calibrating a risk factor model or re-training a solver every time the market conditions change is costly and unsatisfactory. We therefore want to solve PDEs when the environment is not stationary or for several initial conditions at the same time. By learning operators in a single training, we ensure of the robustness of optimal controls with variations of the models, options or constraints. But, ultimately, we want to generalize by solving the PDE with models or conditions that were not present during training. We confirm the effectiveness of the method with several risk management problems by comparing it with other machine learning approaches. We evaluate our DeepOHedger on option pricing tasks, including local volatility models and option spreads involved in energy markets. Finally, we present a purely data-driven approach to risk hedging, from time series generation to learning optimal policiy. Our model then solves a family of parametric PDE from synthetic samples produced by a deep generator previously trained on spot price data from different countries.