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Generative Ornstein-Uhlenbeck Markets via Geometric Deep Learning

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  • Anastasis Kratsios
  • Cody Hyndman

Abstract

We consider the problem of simultaneously approximating the conditional distribution of market prices and their log returns with a single machine learning model. We show that an instance of the GDN model of Kratsios and Papon (2022) solves this problem without having prior assumptions on the market's "clipped" log returns, other than that they follow a generalized Ornstein-Uhlenbeck process with a priori unknown dynamics. We provide universal approximation guarantees for these conditional distributions and contingent claims with a Lipschitz payoff function.

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  • Anastasis Kratsios & Cody Hyndman, 2023. "Generative Ornstein-Uhlenbeck Markets via Geometric Deep Learning," Papers 2302.09176, arXiv.org.
    • Handle: RePEc:arx:papers:2302.09176
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    References listed on IDEAS

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    1. Jim Gatheral & Alexander Schied, 2011. "Optimal Trade Execution Under Geometric Brownian Motion In The Almgren And Chriss Framework," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 353-368.
    2. Sebastian Jaimungal, 2022. "Reinforcement learning and stochastic optimisation," Finance and Stochastics, Springer, vol. 26(1), pages 103-129, January.
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