  We study an optimal execution problem in the presence of market impact where
the security price follows a geometric Ornstein-Uhlenbeck process, which
implies the mean-reverting property, and show that the optimal strategy is a
mixture of initial/terminal block liquidation and gradual intermediate
liquidation. The mean-reverting property describes a price recovery effect that
is strongly related to the resilience of market impact, as described in several
papers that have studied optimal execution in a limit order book (LOB) model.
It is interesting that despite the fact that the model in this paper is
different from the LOB model, the form of our optimal strategy is quite similar
to those obtained for an LOB model. Moreover, we discuss what properties cause
gradual liquidation as an optimal strategy by studying various cases and find
out that not only "convexity of market impact function" but also "price
recovery effect" (or, in other words, transience of market impact) are
essential to make a trader execute the security gradually to mitigate the
effect of market impact.
