通过几何深度学习生成Ornstein-Uhlenbeck市场
Generative Ornstein-Uhlenbeck Markets via Geometric Deep Learning
摘要：
我们考虑用一个机器学习模型同时逼近市场价格及其对数收益的条件分布的问题。我们证明了Kratsios和Papon（2022）的GDN模型的一个实例解决了这个问题，而没有对市场的“修剪”日志回报进行事先假设，除了它们遵循具有先验未知动态的广义Ornstein-Uhlenbeck过程。我们为这些条件分布和具有Lipschitz支付函数的未定权益提供了普遍近似保证。
英文摘要：
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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