Optimal execution with price impact under Cumulative Prospect Theory

Optimal execution of a stock (or portfolio) has been widely studied in academia and in practice over the past decade, and minimizing transaction costs is a critical point. However, few researchers consider the psychological factors for the traders. What are traders truly concerned with - buying low in the paper accounts or buying lower compared to others? We consider the optimal trading strategies in terms of the price impact and Cumulative Prospect Theory and identify some specific properties. Our analyses indicate that a large proportion of the execution volume is distributed at both ends of the transaction time. But the trader's optimal strategies may not be implemented at the same transaction size and speed in different market environments.