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.
翻译:对典型的量化融资问题,许多现代计算方法的制定是尽量减少损失经验,允许直接应用统计机学习的古典成果,这些方法旨在直接建立套期保值或投资决定的最佳反馈代表,在此框架内分析这些方法,表明其有效性和容易发生一般化错误;使用传统技术表明,过度培训使经过培训的投资决定成为预期,并证明大假设空间的过度学习;另一方面,基于Rademacher复杂程度的非零用估计表明,足够大的培训组合趋于一致;这些结果强调合成数据生成的重要性和对复杂模型与市场数据进行适当校准的重要性;一个经过数字研究的典型例子说明了这些可能性,包括问题层面在超学程度方面的重要性,以及这一方法的有效性。