论文标题
财务最小化的经验风险最小化：展望未来
Deep Empirical Risk Minimization in finance: looking into the future
论文作者
论文摘要
定量融资中经典问题的许多现代计算方法被表述为经验损失最小化（ERM），从而可以直接应用统计机器学习的经典结果。这些方法旨在直接构建对冲或投资决策的最佳反馈表示，在此框架中分析了它们的有效性以及它们对概括错误的敏感性。使用古典技术表明，过度训练的渲染训练训练了投资决策，以成为预期的预期，并证明了大型假设空间过度学习。另一方面，基于Rademacher复杂性的非反应估计显示了足够大的训练集的收敛性。这些结果强调了合成数据生成的重要性以及复杂模型对市场数据的适当校准。经过数字研究的风格化示例说明了这些可能性，包括问题维度在过度学习程度上的重要性以及这种方法的有效性。
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.
