# Infinite horizon agent in Avellaneda-Stoikov model

I am trying to understand the Avellaneda-Stoikov model for high frequency trading, in particular the optimizing agent with infinite horizon.

The reservation ask/bid prices for such an agent are defined in the paper as: and It is said in the paper that $\omega$ serves as an upper bound on the inventory position.

I took the argument of the natural logarithm from the reservation bid price and wrote the inequality satisfying the logarithm:

Looking closer at the formula for $\omega$, we see that it depends on some $q_{max}$ parameter.

What I can't answer for myself is the question whether $q_{max}$ is heuristically chosen or is it estimated by some established method.

I'm doing this from memory, but as I recall $$q_{\text{max}}$$ is the maximum inventory on any side that you wish to take (otherwise you might build up a huge position if you are adversely selected).

Later papers such as this one https://arxiv.org/pdf/1105.3115.pdf helped my understanding.

As it actually happens, I implemented these algorithms and had a go doing HFT style MM on Bitmex. Although they do work in certain situations, I'll paraphrase something Sinclair wrote in his book, "Making money market making is trivial. Keeping it is a lot harder." These algos are an interesting starting point, but remember they are based on an idealised distribution of incoming orders, perfect connectivity to the exchange, and always being front-of-the-queue.

• which book was it? Is there any other books or resources that you could recommend as an intro to the practical realities? Thanks! Sep 2 '21 at 16:05
• I believe it was "Option Trading" by Euan Sinclair, full text available here procapital.mohdfaiz.com/books/books-image/mainBook/… In my limited experience, I think it's better to build from trial-and-error and data. The theory doesn't really translate very well to actual trading. Sep 3 '21 at 10:30

if qmax here is a number of shares then qmax+1 does not make any sense to me whatsoever. I think that you have something wrong here.

• This is more of a comment than an answer, no? May 7 '21 at 10:20
• Actually after reading this again the OP seems correct, Qmax is like he said the max number of shares. I think the +1 is just to allow Qmax to go to 0 without breaking the formula (amount 1 assumed too small to matter). Sep 10 '21 at 15:00