I'm working in the Avellaneda-Stoikov implementation using Python. My implementation reproduces the authors' results, but I don't know how to properly adapt the algorithm in order to consider a larger time horizon. From the equation
r = s - q * gamma * sigma**2 * (T-t)
if we use larger T, the indifference price computed could become too big compared with the mid price s, or even a negative value, when q is positive.
Is there an a-dimensional implementation? How to independize from T? Is there a possibility to independize also from the election of s?