  The task we consider is portfolio construction in a speculative market, a
fundamental problem in modern finance. While various empirical works now exist
to explore deep learning in finance, the theory side is almost non-existent. In
this work, we focus on developing a theoretical framework for understanding the
use of data augmentation for deep-learning-based approaches to quantitative
finance. The proposed theory clarifies the role and necessity of data
augmentation for finance; moreover, our theory implies that a simple algorithm
of injecting a random noise of strength $\sqrt{|r_{t-1}|}$ to the observed
return $r_{t}$ is better than not injecting any noise and a few other
financially irrelevant data augmentation techniques.
