  We consider the optimal trade execution strategies for a large portfolio of
single stocks proposed by Almgren (2003). This framework accounts for a
nonlinear impact of trades on average market prices. The results of Almgren
(2003) are based on the assumption that no shares of assets per unit of time
are trade at the beginning of the period. We propose a general solution method
that accomodates the case of a positive stock of assets in the initial period.
Our findings are twofold. First of all, we show that the problem admits a
solution with no trading in the opening period only if additional parametric
restrictions are imposed. Second, with positive asset holdings in the initial
period, the optimal execution time depends on trading activity at the beginning
of the planning period.
