Before revision:  More precisely,  they set prices at which they agree to buy and sell the assets they cover . Market makers face therefore an interesting optimization problem: they need to choose bid and ask prices for making money out of their bid-ask spread while mitigating the risk associated with holding inventory in a volatile market.
After revision:  More precisely, for a list of assets, they set prices at which they agree to buy and sell the assets they cover . Market makers face therefore an interesting optimization problem: they need to choose bid and ask prices for making money out of their bid-ask spread while mitigating the risk associated with holding inventory in a volatile market.