Dynamic optimal execution in a mixed-market-impact Hawkes price model

Understand

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.