Do market makers use machine learning?

Machine Learning

Do market makers use machine learning?

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Today, let’s take a look at a paper by the brilliant Professor Sebastian Jaimungal of the University of Toronto’s Department of Statistics. See our list of Top 10 Machine Learning Minds on Wall Street for 2022 & How to Build a Volatility Surface?

Paper titled: ‘Optimal trading with automated market makers powered by deep learning‘ co-authors and:

Yuri Saporito, Getulio Vargas Foundation (FGV) – EMAp – School of Applied Mathematics. Max O. Souza of the UFF – Universidade Federal Fluminense – Instituto de Matemática e Estatística. UFF’s Yuri Thamsten – Universidade Federal Fluminense – Instituto de Matemática e Estatística

The work focuses on: “Optimization of trading strategies in Constant Function Market Makers (CFMMs) and centralized exchanges. These he developed models to describe the interaction between the two markets and used the concept of conditional eligibility to We estimate the conditional dependencies of

First, what is a “Constant Function Market Maker”?

A constant function market maker (CFMM) is a type of automated market maker (AMM) that provides liquidity to a decentralized exchange (DEX). CFMMs are designed to maintain a constant ratio between the two assets in the liquidity pool, so traders can buy or sell either asset at any time.

Unlike traditional market makers that use equity capital to buy and sell assets to maintain a balanced market, CFMMs use mathematical formulas to determine the price of each asset in the liquidity pool. This formula takes into account the current ratio of each asset and the amount of liquidity in the pool, ensuring that the price of each asset is stable and predictable.

CFMM is particularly suitable for DEX because it can operate autonomously.

As a result, no central authority is required to manage it. This enables trustless transactions between buyers and sellers, resulting in lower transaction fees and faster settlement times.

One of the most popular CFMMs is Uniswap. Launched in 2018, it quickly became one of the most popular DEXs on the cryptocurrency market!

Uniswap uses a variant of the constant function formula known as the x*y=k model. x and y represent the amount of each asset in the pool. Also, k is a constant value determined by the total value of the pool.

CFMM has proven to be a popular and effective way of providing liquidity to DEXs, but it is not without its limitations. Because CFMMs base their asset prices on mathematical formulas, they may not respond quickly to sudden market changes or price fluctuations. Additionally, CFMMs can be vulnerable to manipulation by traders who can take advantage of the formulas.

Furthermore, “we pose an optimal execution problem in which an agent hides orders by controlling the trade rate” and “without approximating the market dynamics. The resulting dynamic programming equations are analytical It is unwieldy, so we use the deep Galerkin method to solve it.”

The Galerkin method is a numerical technique used to solve partial differential equations (PDEs). The name comes from the Russian mathematician Boris his Galerkin, who developed the method in the early 20th century. The Galerkin method is a popular and powerful technique for solving a wide variety of partial differential equations, including elliptic, parabolic, and hyperbolic equations.

Boris Grigorievich Galerkin.jpg
Soviet mathematician Boris Galerkin
i don’t know – Created date: 1941 original publication: i don’t know immediate source:

Roughly speaking, the Galerkin method works by approximating the solution to the partial differential equation using a finite-dimensional subspace of the full solution space.

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Могила академика Бориса Галёркина на Литераторских в Санкт-Pетербурге.
SerSem – homebrew

Usually this subspace is chosen to be spanned by a set of basis functions such as polynomials or trigonometric functions. Basis functions are chosen based on the structure of the PDE and the geometry of the domain in which it is defined.

To apply the Galerkin method, first obtain a weak formulation of the PDE.

This involves multiplying the partial differential equation by a test function, integrating over the entire domain, and applying the integration piece by piece. The resulting equation is a system of linear equations containing the coefficients of the basis functions.

The Galerkin method then chooses an appropriate set of basis functions and solves the resulting system of linear equations for the coefficients. Once the coefficients are obtained, an approximate solution to the PDE is reconstructed by evaluating the basis functions at points within the domain.

The Galerkin method has several advantages over other numerical methods for solving partial differential equations. It is a general method that can be applied to a wide range of problems and is highly accurate when using a sufficiently large number of basis functions. Also, this method has good stability. That is, small errors in the input data or numerical approximations do not cause the solution to diverge.

Despite its advantages, the Galerkin method has some limitations. Specifically, the accuracy of the method depends on the choice of basis functions. Moreover, problems with complex geometries and large domains can be computationally expensive.

In conclusion, the researchers “conduct numerical experiments and show that the optimal strategy is less prone to price drift and outperforms the simple strategy.”

Download Full Paper: Optimal Trading for Automated Market Makers with Deep Learning by Sebastian Jaimungal, Yuri Saporito, Max O. Souza, and Yuri Thamsten :: SSRN

Do market makers use machine learning?

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