NEURALCHAOS: OPTIMAL ADAPTED APPROXIMATION OF SQUARE INTEGRABLE PREDICTABLE PROCESSES

Battle Count: 77

Highly relevant to quantitative trading. The paper directly addresses the core challenge of parameterizing trading strategies (predictable processes) that respect causality (no look-ahead bias) and integrability constraints. The dynamic hedging application in Black-Scholes is directly applicable to derivatives trading. The framework provides a principled way to learn optimal hedging strategies and control processes. The negative result about Markovian neural SDEs being meagre in H2T is important for practitioners who rely on such models. The architecture is compatible with standard deep learning frameworks (PyTorch/TensorFlow).

The architecture uses standard ReLU MLPs which are straightforward to implement in PyTorch/TensorFlow. However, the causal structure requires careful implementation: lower-triangular lifting matrices, row-wise heads, and deterministic time masks. The theoretical understanding of chaoslet expansions, Haar coordinates, and Malliavin-Sobolev spaces adds conceptual complexity. The training pipeline requires generating Brownian motion samples and computing the H2T norm loss. The GitHub code is provided, reducing practical implementation barriers.

Code is publicly available on GitHub (https://github.com/AnastasisKratsios/CausalTransformer). Experiments use synthetic Brownian motion data with specified parameters (T=1, M=101 grid points, S=10^4 samples). Architecture hyperparameters are fully specified (K_lift=30, Head Width=20, Head Depth=2, epochs=200). However, no pre-trained models or exact random seeds are mentioned, and the theoretical proofs are extensive.