  In this paper, we introduce a suite of models for price-aware automated
market making platforms willing to optimize their quotes. These models
incorporate advanced price dynamics, including stochastic volatility, jumps,
and microstructural price models based on Hawkes processes. Additionally, we
address the variability in demand from liquidity takers through models that
employ either Hawkes or Markov-modulated Poisson processes. Each model is
analyzed with particular emphasis placed on the complexity of the numerical
methods required to compute optimal quotes.
