Optimal solution of the liquidation problem under execution and price impact risks

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Trading Strategies
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Francesca Mariani and Lorella Fatone
We consider an investor that trades continuously and wants to liquidate an initial asset position within a prescribed time interval. As a consequence of his trading activity during the execution of the liquidation order the investor has no guarantees that the placed order is executed immediately; it may go unfilled partially filled or filled in excess. The uncertainty in the execution affects the trading activity of the investor and the asset share price dynamics generating additional sources of noise: the execution risk and the price impact risk respectively. Assuming the two sources of noise correlated and driven by the cumulative effect of the investor trading strategy we study the problem of finding the optimal liquidation strategy adopted by the investor in order to maximize the expected revenue resulting from the liquidation. The mathematical model of the liquidation problem presented here extends the model of Almgren and Chriss [Optimal execution of portfolio transactions. J. Risk 2000 3(2) 5–39] to include execution and price impact risks. The liquidation problem is modeled as a linear quadratic stochastic optimal control problem with the finite horizon and under some assumptions about the functional form for the magnitude of execution and price impact risks is solved explicitly. The derived solution coincides with the optimal trading strategy obtained in the absence of execution uncertainty for an asset price with a modified growth rate. This suggests that the uncert
Year Published
Quantitative Finance 2022 vol. 22 issue 6 1037-1049