  We consider an investor that trades continuously and wants to liquidate an
initial asset position within a prescribed time interval. During the execution
of the liquidation order the investor is subject to execution risk. 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. We
present a mathematical model of the liquidation problem that extends the model
of Almgren and Chriss (Almgren, R., Chriss, N., Optimal execution of portfolio
transactions, Journal of Risk, 2000) to include execution risk. The liquidation
problem is modeled as a linear quadratic stochastic optimal control problem
with finite horizon and, under some hypotheses, is solved explicitly.
