Price impact refers to the empirical observation that executing a large order adversely and persistently affects a risky asset’s price, leading to less favorable execution costs. Propagator models are a central tool for describing these phenomena mathematically. They express price movements in terms of the influence of past trades and thus capture the decay of price impact following each trade.

Results on optimal order execution and optimal portfolio choice in this area have been scarce. In particular, the power-law decay of price impact renders the associated stochastic control problems non-Markovian and time-inconsistent. In this talk, we present recent developments in optimal execution, cross-impact, and price manipulation, as well as price impact games based on the propagator model. Finally, we discuss nonparametric estimation of the propagator using datasets that contain correlated price trajectories, trading signals, and metaorders.

Personal website of Eyal Neuman