Optimal Trading on a Dynamic Curve Automated Market Maker
Optimal Trading on a Dynamic Curve Automated Market Maker
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动态曲线自动做市商的最优交易
DOI：
10.1109/icbc54727.2022.9805489
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
B. Krishnamachari
中科院分区：
文献类型：
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作者：
Shuang Wang;B. Krishnamachari
在新兴的去中心化金融（DeFi）领域，Uniswap和Curve等主要平台使用的大多数现有的自动做市商（AMM）协议都是由静态数学方程（如常数产品曲线）控制的。这些曲线的一个主要缺点是它们需要外力来维持流动性池（LP）的价格，使LP因套利而遭受损失。最近提出了一种新的解决方案，即动态曲线AMM，以确保池价格始终与市场价格匹配，使LP不受套利者的攻击。然而，动态曲线有一个路径依赖的交易问题，这意味着交易的数量和交易的分布会影响交易者的收益。我们展示了如何在几种设置下找到动态AMM曲线的最优交易策略。我们首先证明了在零交易费的情况下，最优交易策略是进行无限小的交易，从而导致零滑差。然后，我们给出了一个在固定交易数设置下计算最优策略的算法。虽然这个问题的搜索空间是指数级的，但我们的算法利用动态规划来实现多项式的运行时间。最后，我们将解决方案推广到更复杂的设置，包括每订单费用设置和百分比费用设置。
In the emerging realm of decentralized finance (DeFi), most of the existing Automated Market Maker (AMM) protocols used by major platforms like Uniswap and Curve are governed by a static mathematical equation, such as the constant product curve. One major shortcoming of these curves is that they require external forces to maintain the price of the liquidity pool (LP), subjecting the LP to loss due to arbitrage. A novel solution, the dynamic curve AMM, was recently proposed to ensure that the pool price always matches the market price, making the LP invulnerable to arbitrageurs. Dynamic curves, however, have a path-dependent trading problem, meaning that the number of trades and the distribution of trades affect the trader’s gain. We show how to find the optimal trading policy for a dynamic AMM curve under several settings. We first show that in a zero-transaction-fee setting the optimal trading policy is to place infinitesimally small trades, resulting in zero slippage. Then, we present an algorithm that computes the optimal policy in a fixed-number-of-trade setting. Though the problem has an exponentially large search space, our algorithm utilizes dynamic programming to achieve a polynomial run-time. Finally, we generalize the solution to more complex settings, including a per-order-fee setting and a percentage-fee setting.