  We provide an explicit characterization of the optimal market making strategy
in a discrete-time Limit Order Book (LOB). In our model, the number of filled
orders during each period depends linearly on the distance between the
fundamental price and the market maker's limit order quotes, with random slope
and intercept coefficients. The high-frequency market maker (HFM) incurs an
end-of-the-day liquidation cost resulting from linear price impact. The optimal
placement strategy incorporates in a novel and parsimonious way forecasts about
future changes in the asset's fundamental price. We show that the randomness in
the demand slope reduces the inventory management motive, and that a positive
correlation between demand slope and investors' reservation prices leads to
wider spreads. Our analysis reveals that the simultaneous arrival of buy and
sell market orders (i) reduces the shadow cost of inventory, (ii) leads the HFM
to reduce price pressures to execute larger flows, and (iii) introduces
patterns of nonlinearity in the intraday dynamics of bid and ask spreads. Our
empirical study shows that the market making strategy outperforms those which
ignores randomness in demand, simultaneous arrival of buy and sell market
orders, and local drift in the fundamental price.
