We consider a single security market based on a limit order book and two investors, with different speeds of trade execution. If the fast investor can front-run the slower investor, we show that this allows the fast trader to obtain risk free profits, but that these profits cannot be scaled. We...

We relate models based on costs of switching beliefs (e.g. due to inattention) to hypothesis tests. Specifically, for an inference problem with a penalty for mistakes and for switching the inferred value, a band of inaction is optimal. We show this band is equivalent to a confidence interval,...

Modelling joint dynamics of liquid vanilla options is crucial for arbitrage-free pricing of illiquid derivatives and managing risks of option trade books. This paper develops a nonparametric model for the European options book respecting underlying financial constraints and while being...

Machine learning models are increasingly used in a wide variety of financial settings. The difficulty of understanding the inner workings of these systems, combined with their wide applicability, has the potential to lead to significant new risks for users; these risks need to be understood and...

The Asymptotic Randomised Control (ARC) algorithm provides a rigorous approximation to the optimal strategy for a wide class of Bayesian bandits, while retaining reasonable computational complexity. In particular, it allows a decision maker to observe signals in addition to their rewards, to...