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In the article A High Frequency Trade Execution Model for Supervised Learning, Matthew Dixon refers to two Market Making Strategies MM1 and MM2 without specifying their true natures.

Definition 4.0.1 (Strategy) : A strategy is a $n$-vector function $L: \mathbb{R}^{+} \times \mathbb{Z} \cap (-m, m] \to \mathbb{Z}^{n}$ of the form $L_{t}(\hat{Y}_{t})$, where $t$ denotes the time that the trade is placed. Based on the predicted value of $\hat{Y}_{t}$, the strategy quotes on either the bid and ask at one or more price levels.

Definition 4.0.2 (Market Making Strategy) : A market making strategy is the pair $L_{t} = (L^{a}_{t}, L^{b}_{t})$ representing the quoting of a bid and ask at time $t$.

Can you tell me which Market Making Strategy (MMS) he is referring to? Otherwise, what would be a good MMS in relation to the previous definitions? Any article?

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Unfortunately, with the info given, he isn't referring to any specific MMS at all. He is actually just defining some basic properties that are pretty straight forward.

In Definition 4.0.1 & 4.0.2 he defines an n-vector in a bounded area and states that a strategy is just "something" execute at some time "t" given some prediction. He follows by including some bid/ask variables to his previous statement, this doesn't tell us much (most of this you already know), hence the reason why he isn't specific about anything.

Here is a list of some well known types of HFT/MMS with lots of online resources:

  1. Order flow prediction HFT strategies
  2. Execution HFT Strategies
  3. Liquidity Provisioning – Market Making strategies
  4. Automated HFT Arbitrage strategies

For those who are new to HFT, I suggest reading this quick article, it breaks down HFT and how it works without getting too complicated:

https://www.quantinsti.com/blog/automated-market-making-overview/

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  • $\begingroup$ What are the best best strategy for low number of transactions per day? For example, the number of transactions may approach that of a trader experiment and not that of a bank or fund manager. $\endgroup$ – Jeremie Apr 23 '18 at 0:30

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