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