Kavli Affiliate: Cheng Peng
| First 5 Authors: Xue Cheng, Peng Guo, Tai-ho Wang, ,
| Summary:
The paper addresses the problem of meta order execution from a
broker-dealer’s point of view in Almgren-Chriss model under execution risk. A
broker-dealer agency is authorized to execute an order of trading on some
client’s behalf. The strategies that the agent is allowed to deploy is subject
to a benchmark, referred to as the reference strategy, regulated by the client.
We formulate the broker’s problem as a utility maximization problem in which
the broker seeks to maximize his utility of excess profit-and-loss at the
execution horizon, of which optimal feedback strategies are obtained in closed
form. In the absence of execution risk, the optimal strategies subject to
reference strategies are deterministic. We establish an affine structure among
the trading trajectories under optimal strategies subject to general reference
strategies using implementation shortfall (IS) and target close (TC) orders as
basis. Furthermore, an approximation theorem is proposed to show that with
small error, general reference strategies can be approximated by piece-wise
constant ones, of which the optimal strategy is piece-wise linear combination
between IS and TC orders. We conclude the paper with numerical experiments
illustrating the trading trajectories as well as histograms of terminal wealth
and utility at investment horizon under optimal strategies versus those under
TWAP strategies.
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