Title: Optimal Trading in Automatic Market Makers with Deep Learning Show Chinese title

Title: 带有深度学习的自动做市商中的最优交易

Abstract: This article explores the optimisation of trading strategies in Constant Function Market Makers (CFMMs) and centralised exchanges. We develop a model that accounts for the interaction between these two markets, estimating the conditional dependence between variables using the concept of conditional elicitability. Furthermore, we pose an optimal execution problem where the agent hides their orders by controlling the rate at which they trade. We do so without approximating the market dynamics. The resulting dynamic programming equation is not analytically tractable, therefore, we employ the deep Galerkin method to solve it. Finally, we conduct numerical experiments and illustrate that the optimal strategy is not prone to price slippage and outperforms na\"ive strategies. Show Chinese abstract

Abstract: 本文探讨了在恒定函数做市商（CFMM）和集中式交易所中的交易策略优化。我们建立了一个考虑这两个市场之间相互作用的模型，使用条件可获取性的概念来估计变量之间的条件依赖性。此外，我们提出了一个最优执行问题，其中代理通过控制交易速率来隐藏其订单。我们没有对市场动态进行近似。 resulting dynamic programming equation 不是解析可处理的，因此，我们采用深度Galerkin方法来解决它。最后，我们进行了数值实验并说明最优策略不易受到价格滑点的影响，并优于简单策略。