Optimal VWAP Strategies under Regime Switching

In this paper, we analyze the problem of trading a large position in the market place when the stock price dynamic follows a regime switching process. In this work, we are particularly interested in trading algorithms that track the market benchmark known as the volume-weighted average price (VWAP). We propose a trading algorithm that breaks the execution order into small pieces and executes them over a predetermined period of time so as to maximize its VWAP or possibly exceed the overall market 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.