mlsanityData to 13 Oct 2026

Chaotic Hedging with Iterated Integrals and Neural Networks

arXiv 2209.10166 ↗First posted 21 Sep 2022q-fin.MF cs.LG math.PRcited by 10

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Abstract (arXiv)

In this paper, we derive an Lp-chaos expansion based on iterated Stratonovich integrals with respect to a given exponentially integrable continuous semimartingale. By omitting the orthogonality of the expansion, we show that every p-integrable functional, p ∈ [1,∞), can be approximated by a finite sum of iterated Stratonovich integrals. Using (possibly random) neural networks as integrands, we therefere obtain universal approximation results for p-integrable financial derivatives in the Lp-sense. Moreover, we can approximately solve the Lp-hedging problem (coinciding for p = 2 with the quadratic hedging problem), where the approximating hedging strategy can be computed in closed form within short runtime.

Key facts. Cited by 10 papers in the map (data through 13 Oct 2026). Builds on 17 of its 116 references that are in the map. First posted on arXiv 21 Sep 2022.

Builds on

17 of 116 references.

References · 17

  1. 2017Solving high-dimensional partial differential equations using deep learningcited by 550
  2. 2018Deep Hedgingcited by 106
  3. 2017Optimal Approximation with Sparsely Connected Deep Neural Networkscited by 91
  4. 2018Echo state networks are universalcited by 87
  5. 2016Kernels for sequentially ordered datacited by 83
  6. 2018Universal features of price formation in financial markets: perspectives from Deep Learningcited by 59
  7. 2020Approximation Bounds for Random Neural Networks and Reservoir Systemscited by 52
  8. 2019Neural networks for option pricing and hedging: a literature reviewcited by 39
  9. 2021Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionalitycited by 34
  10. 2020A generative adversarial network approach to calibration of local stochastic volatility modelscited by 29
  11. 2020Non-Euclidean Universal Approximationcited by 29
  12. 2020Discrete-time signatures and randomness in reservoir computingcited by 23
5 more
  1. 2022Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformercited by 22
  2. 2018Robust risk aggregation with neural networkscited by 6
  3. 2019Robust pricing and hedging of options on multiple assets and its numericscited by 6
  4. 2021A deep learning approach to data-driven model-free pricing and to martingale optimal transportcited by 6
  5. 2022Detecting data-driven robust statistical arbitrage strategies with deep neural networkscited by 4

Built on by

Cited by year (2026 to 13 Oct)

Citing papers per year: 2022: 2; 2023: 4; 2024: 2; 2025: 1; 2026: 1.

10 papers.

  1. 2022Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysiscited by 22
  2. 2023Global universal approximation of functional input maps on weighted spacescited by 19
  3. 2023A Brief Survey on the Approximation Theory for Sequence Modellingcited by 15
  4. 2023Universal approximation property of Banach space-valued random feature models including random neural networkscited by 13
  5. 2024Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEscited by 12
  6. 2023Infinite-dimensional reservoir computingcited by 7
  7. 2025Generative Neural Operators of Log-Complexity Can Simultaneously Solve Infinitely Many Convex Programscited by 7
  8. 2024Solving stochastic partial differential equations using neural networks in the Wiener chaos expansioncited by 6
  9. 2022Langevin dynamics based algorithm e-THvarepsilonO POULA for stochastic optimization problems with discontinuous stochastic gradientcited by 5
  10. 2026NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processescited by 0