Chaotic Hedging with Iterated Integrals and Neural Networks

@article{Neufeld2022ChaoticHW,
  title={Chaotic Hedging with Iterated Integrals and Neural Networks},
  author={Ariel Neufeld and Philipp Schmocker},
  journal={ArXiv},
  year={2022},
  volume={abs/2209.10166}
}
A BSTRACT . In this paper, we extend the Wiener-Ito chaos decomposition to the class of diffusion processes, whose drift and diffusion coefficient are of linear growth. By omitting the orthogonality in the chaos expansion, we are able to show that every p -integrable functional, for p ∈ [1 , ∞ ) , can be represented as sum of iterated integrals of the underlying process. Using a truncated sum of this expansion and (possibly random) neural networks for the integrands, whose parameters are learned… 

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