Standard two-dimensional Brownian motion is a random process in the plane whose components are independent one-dimensional Brownian motions. However, it is also possible to define such a process with correlation between the components, and this is known as correlated Brownian motion. Motivation for considering this process has come from finance, in particular in the pricing of exotic options. In an interesting recent preprint, the exit distribution of correlated Brownian motion from a disk was calculated by applying a transform in order to create a new problem involving standard Brownian motion, which was tractable. This method seems to admit considerable extension, and the purpose of this project is to study it and related topics, hoping to find new situations in which the method can be applied.
Pu Ti is an undergraduate mathematics student at Monash University with an interest in probability, statistics and mathematical finance. He has a background in machine learning and previously studied civil engineering before his interest in mathematics got the better of him. In his spare time, he has a rather niche hobby of translating Chinese web novels into English.