Deep Empirical Risk Minimization in finance: looking into the future
This work highlights the importance of generalization error and overlearning in deep ERM for financial decision-making, particularly for practitioners developing investment and hedging strategies.
This paper examines deep empirical risk minimization (ERM) in quantitative finance, showing that while effective, these methods are susceptible to generalization error. Over-training leads to anticipative investment decisions, and overlearning is proven for large hypothesis spaces, though non-asymptotic estimates indicate convergence with sufficiently large training sets.
Many modern computational approaches to classical problems in quantitative finance are formulated as empirical loss minimization (ERM), allowing direct applications of classical results from statistical machine learning. These methods, designed to directly construct the optimal feedback representation of hedging or investment decisions, are analyzed in this framework demonstrating their effectiveness as well as their susceptibility to generalization error. Use of classical techniques shows that over-training renders trained investment decisions to become anticipative, and proves overlearning for large hypothesis spaces. On the other hand, non-asymptotic estimates based on Rademacher complexity show the convergence for sufficiently large training sets. These results emphasize the importance of synthetic data generation and the appropriate calibration of complex models to market data. A numerically studied stylized example illustrates these possibilities, including the importance of problem dimension in the degree of overlearning, and the effectiveness of this approach.