Many natural phenomena are modelled by a stochastic process. Since no model can be completely correct, it is useful to be able to measure the difference between the model and reality. In this talk, we will look at an appropriate notion of distance between two discrete-time stochastic processes. This distance comes from a variation of optimal transport, a classical problem in analysis. We will see how this distance can be applied to optimal stopping problems, and if there’s time we’ll discuss extending it to cover continuous-time processes like Brownian motion. This is the topic that I’m starting to work on in my postdoc. Everything I will talk about is work done by someone else (usually some of my colleagues in Vienna) and I’m no expert in this, so the talk should be a (fairly) accessible introduction!