We study how a broker provides liquidity to an informed trader and to a noise trader. The broker decides how much of the flow she keeps in her books (i.e., internalisation) and how much she unwinds in an exchange (i.e., externalisation). We frame the interactions between the broker and traders as a Stackelberg game. The informed trader knows the stochastic process that drives the drift of the asset price. The order flow of the noise trader is uninformative. We obtain the broker's internalisation and externalisation optimal strategy in closed-form. Model parameters are estimated from market data and we show the performance of the broker, the noise trader, and the informed trader for a variety of scenarios. Lastly, we compute the amount of transaction costs that the broker needs to charge to break even.

Bio: Leandro Sánchez-Betancourt is an applied mathematician based at King's College London. He obtained his PhD in 2021 at the University of Oxford under the supervision of Álvaro Cartea. Before taking up a lectureship in financial mathematics at King's, he was a research associate at Imperial College London. He is interested in a number of problems surrounding mathematical finance, in particular, building mathematical models that help understand trading behaviour.