Time：14:00-15:00, Thursday, April 16 2026
Venue：E14-301
Speaker：Benjamin Michael Hambly，University of Oxford
Title：Stochastic Stefan problems and limit order books
Abstract：In electronic financial markets buyers and sellers post orders indicating how many units of asset they are prepared to buy or sell and at what price. The collection of all these posted orders is called the limit order book. Those who need to trade then take the best available price for either buying or selling. This mechanism gives rise to the evolution of asset prices that we see. From a simple model for the arrival and cancellation of limit orders, and taking scaling limits, we will show how it may be natural to model the limit order book as a stochastic Stefan problem. The Stefan problem arises as a model for the evolution of the temperature in two phases of a material. It is a partial differential equation with a free boundary describing the interface between the phases. By regarding the sides of the order book as different phases and driving them with white noise we can model the whole system as a pair of coupled stochastic partial differential equations and the price of the asset is then the interface between the phases. We will discuss the existence, uniqueness and properties of the motion of the interface for this stochastic Stefan problem.
