Dynamic Trading: Price Inertia and Front-Running

We build a linear-quadratic model to analyze trading in a market with private information and heterogeneous agents. Agents receive private inventory shocks and trade continuously. Agents differ in their need for trade as well as size, i.e. the cost to stay away from their ideal positions. In equilibrium, trade is gradual. Trading speed depends on the number and market power of participants, and trade among large market participants is slower than that among small investors. Price has momentum due to the actions of large traders: it drifts down if the sellers have greater market power than buyers, and vice versa. The model captures welfare: it can answer questions about the social costs and benefits of high-frequency traders, the welfare consequences of market consolidation, and many others.