Recent empirical evidence on tradersorder submission strategies in elec-tronic limit order markets (LOB) shows the growing use of hidden orders. This paper provides a theory of the optimal order submission strategies in an LOB, where traders can choose among limit, market and hidden orders. The dynamic model we propose allows traders to take the simultaneous three-dimensional strategic choice of price, quantity and exposure. Traders use hidden orders both to compete for the provision of liquidity and to avoid picking-o ¤ risk. The use of hidden orders increases with order size and rela-tive depth on the opposite side of the market, while it decreases with time-to-shock. Hidden orders increase market depth but could reduce competition in the...