Before revision: The job of market makers is to provide liquidity to other market participants. The main source of risk for market makers is holding inventory and the uncertainty of future price variation. In many cases, the market makers are in charge of a large range of assets . However, managing the risk in multiple asset cases is an important task. We propose in this paper closed-form approximations for the bid and ask quotes a market maker should set for optimally managing the risk of his/her multi-asset market making book.
After revision: 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 bid and ask quotes a market maker should set for optimally managing the risk of his/her multi-asset market making book.