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I have been studying limit order books with focus on the optimal quoting problem for market makers. I have read the Avellaneda-Stoikov model and the subsequent developments. However I am unable to find any papers that quote on multiple levels. It would be very helpful if someone could point me towards such papers.

Thanks!!!!

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I do not think they are such paper, but it is not very different; just pay attention that if you own two orders on the same side of the book, if the further away (from the mid) is executed, then the closest will be executed before.

You will probably first need to study in detail the influence of the order of your orders in the queue. That for, I advice to have a look at L, Othmane Mounjid, and Mathieu Rosenbaum. "Optimal liquidity-based trading tactics." Stochastic Systems 11, no. 4 (2021): 368-390.

It is good to understand this mechanism because maintaining two orders on the same side of the book will essentially allow you to

  1. get a way to be next in the row once a limit will have been fully depleted
  2. maintain a probability of execution that is finer that what only one order can provide you. You will get more control on the expected executed quantity and the price at which it will be executed.

An important take away of this paper is that conditionally to the fact that you obtain an execution, you may have been adversely selected, hence your benchmark price to compare your trade with should not be the mid-price but your best guess for "the price at infinity".

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