  In this work we study the optimal execution problem with multiplicative price
impact in algorithm trading, when an agent holds an initial position of shares
of a financial asset. The inter-selling-decision times are modelled by the
arrival times of a Poisson process. The criterion to be optimised consists in
maximising the expected net present value of gains of the agent, and it is
proved that an optimal strategy has a barrier form, depending only on the
number of shares left and the level of asset price.
