Mathematical Finance (q-fin.MF)

Abstract: We propose the macroscopic market making model \`a la Avellaneda-Stoikov, using continuous processes for orders instead of discrete point processes. The model intends to bridge a gap between market making and optimal execution problems, while shedding light on the influence of order flows on the strategy. We demonstrate our model through three problems. The study provides a comprehensive analysis from Markovian to non-Markovian noises and from linear to non-linear intensity functions, encompassing both bounded and unbounded coefficients. Mathematically, the contribution lies in the existence and uniqueness of the optimal control, guaranteed by the well-posedness of the Hamilton-Jacobi-Bellman equation or the (non-)Lipschitz forward-backward stochastic differential equation.