  Starting from the Avellaneda-Stoikov framework, we consider a market maker
who wants to optimally set bid/ask quotes over a finite time horizon, 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 under full information, 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 market maker needs to adjust for additional regime
uncertainty in terms of P&L sensitivity and observed order flow volatility.
This effect becomes higher, the longer the waiting time in between orders.
