Optimal algorithms for trading large positions

In this paper, we are concerned with the problem of efficiently trading a large position on the market place. If the execution of a large order is not dealt with appropriately this will certainly break the price equilibrium and result in large losses. Thus, we consider a trading strategy that breaks the order into small pieces and execute them over a predetermined period of time so as to minimize the overall execution shortfall while matching or exceeding major execution benchmarks such as the volume-weighted average price (VWAP). The underlying problem is formulated as a discrete-time stochastic optimal control problem with resource constraints. The value function and optimal trading strategies are derived in closed form. Numerical simulations with market data are reported to illustrate the pertinence of these results.