Closed-form Approximations in Multi-asset Market Making

A large proportion of market making models derive from the seminal model Avellaneda and Stoikov. The numerical approximation value function optimal quotes in these remains a challenge when number assets is large. In this article, we propose closed-form approximations for functions many multi-asset extensions Avellaneda–Stoikov model. These or proxies can be used (i) as heuristic evaluation functions, (ii) initial reinforcement learning algorithms, and/or (iii) directly to design quoting strategies through greedy approach. Regarding latter, our results lead new easily interpretable quotes, both finite-horizon case asymptotic (ergodic) regime.