Extensions of the Almgren-Chriss framework

In this short chapter, we present several extensions of the Almgren-Chriss framework. In the first section, we focus on some very basic generalizations of the model. We show that the trader can incorporate his views on the future behavior of the market price of the stock. In particular, we show that a drift can very easily be added. Furthermore, we show that the volatility parameter σ can easily be replaced by a volatility process (σt)t, as long as this process is deterministic. In the second section, we show how participation constraints can be added, for avoiding trading too fast. In the third section, we generalize the Almgren-Chriss framework to the case of a multi-stock portfolio. We cover the case of IS orders, but TC or VWAP orders can be tackled in the same way.