Replicating market makers
Replicating market makers
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复制做市商
DOI：
10.1007/s42521-023-00082-0
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Tarun Chitra
中科院分区：
文献类型：
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作者：
Guillermo Angeris;A. Evans;Tarun Chitra
我们提出了一种方法来构造常数函数做市商（CFUES）的投资组合价值函数匹配的期望回报。更具体地说，我们证明了凹的，非负的，不减的，1-齐次支付函数的空间和凸CFMM的空间是等价的;换句话说，每个CFMM都有一个凹的，非负的，不减的，1-齐次支付函数，并且每个具有这些性质的支付函数都有一个相应的凸CFMM。我们展示了一个简单的方法来恢复CFMM交易功能，产生这种期望的回报。这种方法只使用凸分析的基本工具，并且与Fenchel共轭密切相关。我们证明了我们的结果，通过构建交易功能对应的基本收益，以及标准的金融衍生工具，如期权和掉期。
We present a method for constructing constant function market makers (CFMMs) whose portfolio value functions match a desired payoff. More specifically, we show that the space of concave, nonnegative, nondecreasing, 1-homogeneous payoff functions and the space of convex CFMMs are equivalent; in other words, every CFMM has a concave, nonnegative, nondecreasing, 1-homogeneous payoff function, and every payoff function with these properties has a corresponding convex CFMM. We demonstrate a simple method for recovering a CFMM trading function that produces this desired payoff. This method uses only basic tools from convex analysis and is intimately related to Fenchel conjugacy. We demonstrate our result by constructing trading functions corresponding to basic payoffs, as well as standard financial derivatives, such as options and swaps.