Algorithmic trading and stochastic integration
Abstract
We study simple predictable processes whose coefficients are represented by neural networks. On finite measure spaces, we establish density results for neural networks in Orlicz spaces. For filtrations generated by a stochastic process, measurable random variables, including at stopping times, can be approximated by neural networks depending on finitely many observations. Every stochastic integral with respect to a semimartingale can then be approximated, in the semimartingale topology, by integrals of such simple predictable processes. We show that restricting trading strategies to this class leaves the minimal mean-variance hedging error under partial information unchanged and obtain a no-free-lunch characterization in terms of equivalent martingale measures. Finally, the Bichteler-Dellacherie characterization of semimartingales remains valid even upon restricting the predictable integrands to those whose coefficients are represented by neural networks.
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BibTeX
@misc{arandjelovic2026algorithmic,
title = {{Algorithmic trading and stochastic integration}},
author = {Aleksandar Arandjelovic and Uwe Schmock},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31578},
eprint = {2609.31578},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31578},
}
RIS
TY - UNPB
TI - Algorithmic trading and stochastic integration
AU - Aleksandar Arandjelovic
AU - Uwe Schmock
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31578
UR - https://arxiv.org/abs/2609.31578
AB - We study simple predictable processes whose coefficients are represented by neural networks. On finite measure spaces, we establish density results for neural networks in Orlicz spaces. For filtrations generated by a stochastic process, measurable random variables, including at stopping times, can be approximated by neural networks depending on finitely many observations. Every stochastic integral with respect to a semimartingale can then be approximated, in the semimartingale topology, by integrals of such simple predictable processes. We show that restricting trading strategies to this class leaves the minimal mean-variance hedging error under partial information unchanged and obtain a no-free-lunch characterization in terms of equivalent martingale measures. Finally, the Bichteler-Dellacherie characterization of semimartingales remains valid even upon restricting the predictable integrands to those whose coefficients are represented by neural networks.
ER -