Optimal Execution Problem for Geometric Ornstein-Uhlenbeck Price Process

Details Optimal Execution Problem for Geometric Ornstein-Uhlenbeck Price Process Optimal Execution Problem for Geometric Ornstein-Uhlenbeck Price Process

2011-07-09

arxiv.org/abs/1107.1787v1

Economy

Quantitative Finance

Trading and Market Microstructure

10 pages, 4 figures

Scientific paper

We study the optimal execution problem in the presence of market impact and give a generalization of the main result of Kato(2009). Then we consider an example where the security price follows a geometric Ornstein-Uhlenbeck process which has the so-called mean-reverting property, and then show that an optimal strategy is a mixture of initial/terminal block liquidation and intermediate gradual liquidation. When the security price has no volatility, the form of our optimal strategy is the same as results of Obizhaeva and Wang(2005) and Alfonsi et al.(2010), who studied the optimal execution in a limit-order-book model.

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