  We study a linear price impact model including other liquidity takers, whose
flow of orders either follows a Poisson or a Hawkes process. The optimal
execution problem is solved explicitly in this context, and the closed-formula
optimal strategy describes in particular how one should react to the orders of
other traders. This result enables us to discuss the viability of the market.
It is shown that Poissonian arrivals of orders lead to quite robust Price
Manipulation Strategies in the sense of Huberman and Stanzl. Instead, a
particular set of conditions on the Hawkes model balances the self-excitation
of the order flow with the resilience of the price, excludes Price Manipulation
Strategies and gives some market stability.

Trading and Market Microstructure