31-JAN-2026
We study optimal market making in a limit order book where the dealer faces inventory risk and adverse selection from informed traders, following the Avellaneda–Stoikov (2008) framework extended to include asymmetric information costs. The dealer controls bid and ask quote depths to maximise expected terminal wealth minus a quadratic inventory penalty, leading to a Hamilton–Jacobi–Bellman equation whose solution yields closed-form reservation prices and optimal spreads. The reservation price shifts linearly with inventory and remaining horizon, while the optimal spread decomposes into a risk-aversion compo nent proportional to γσ 2 τ and an adverse-selection component γ2 ln 1 + κγ . Simulated inventory paths under the optimal policy exhibit mean-reverting behaviour governed by the asymmetric quoting rule, with the dealer widening quotes on the side that would exacerbate a large inventory position.
