Optimal execution for a risk-averse trader

Abstract

We solve optimal stochastic control problems for a risk-averse trader who uses market orders and/or limit orders to liquidate a large position in a risky asset. In each case we aim to maximise terminal wealth, while managing the loss due to the price impact of our own trader’s trading activity. We solve the problems using various utility functions for the trader’s risk-aversion and penalty functions for the trader’s urgency to liquidate the position and reduce market risk. We compare and contrast the performance of the strategies, and compare them to industry benchmarks such as TWAP and VWAP.