Price-Aware Automated Market Makers: Models Beyond Brownian Prices and Static Liquidity

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.