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 the 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. Our work is an extension of the paper ``Optimal market making'' by O. Gueant. Here, we consider the case in which the reference price is modeled with a drift and adverse selection; we also study generalizations with asymmetric arrival rate intensities.