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Optimal Execution of Backstopped Block Trades Open Access


Other title
Mathematical Finance
Algorithm Trading
Optimal Execution
Type of item
Degree grantor
University of Alberta
Author or creator
Lin, Xuran
Supervisor and department
Frei, Christoph (Mathematical and Statistical Sciences)
Examining committee member and department
Melnikov, Alexander (Mathematical and Statistical Sciences)
Frei, Christoph (Mathematical and Statistical Sciences)
Choulli, Tahir (Mathematical and Statistical Sciences)
Smith, Gary (Alberta School of Business)
Department of Mathematical and Statistical Sciences
Mathematical Finance
Date accepted
Graduation date
2016-06:Fall 2016
Master of Science
Degree level
In this thesis, we introduce and study a model for a broker who executes a client order and takes over its execution risk at some transition time. Such agreements between clients and brokers are often called backstopped trades. To minimize risk, it may be beneficial for the broker to trade on his/her own book, even before taking over the execution risk of the order. The broker is not allowed to trade in the same stock while executing on behalf of the client, but the broker may trade in a different, correlated stock. We formulate this question as a mean-variance optimization problem with two correlated stocks, also incorporating permanent and temporary market impacts. We consider this problems in three different cases. In the first case, we assume that the transition time is deterministic. We then manage to find an explicit formula for the optimal trading strategy and analyze it in a numerical example. In the second case, we consider a stochastic transition time, but restrict the analysis to deterministic strategies. Under this assumption, we can characterize the optimal trading strategy through an ordinary differential equation. Finally, in the most general case of a stochastic transition time with stochastic strategies, we derive the Hamilton-Jacobi-Bellman equation corresponding to the optimization problem and describe a numerical implementation to find an approximate solution.
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
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