On execution strategies and minimum discrimination information principle

Abstract

Execution strategies are algorithms used to execute huge amount of orders in stock exchanges. Consequently, they are very important for big players such as institutional investors, asset management firms, pension funds and, so on. In this context, there is a plethora of execution algorithms used by traders and brokers to execute the orders of their clients. In this paper, we define execution strategies as execution density functions. We propose an execution impact cost function based on Kullback-Leibler divergence to be used in the derivation of execution strategies in general. Time weighted average price (TWAP) and volume weighted average price (VWAP) execution strategies are the two fundamental algorithms that originate several other strategies. Formally, we derive the TWAP and VWAP strategies using the minimum discrimination information principle. Additionally, we use the developed theory to obtain some VWAP tilt execution strategies.