Abstract: Starting from the Avellaneda--Stoikov framework, we consider a market maker who wants to optimally set bid/ask quotes over a finite time interval, to maximize her expected utility. The intensities of the orders she receives depend not only on the spreads she quotes, but also on unobservable factors modelled by a hidden Markov chain. We tackle this stochastic control problem under partial information with a model that unifies and generalizes many existing ones, combining several risk metrics and constraints, and using general decreasing intensity functionals. We use stochastic filtering, control and piecewise-deterministic Markov processes theory, to reduce the dimensionality of the problem and characterize the reduced value function as the unique continuous viscosity solution of its dynamic programming equation. We then solve the analogous full information problem and compare the results numerically through a concrete example. We show that the optimal full information spreads are biased when the exact market regime is unknown, and the MM needs to adjust for `regime risk' in terms of liquidity volatility and sensitivity to regime changes. This effect becomes higher the longer the waiting time in between orders.

The talk is based on a joint paper with D. Zabaljauregui (LSE).