Brownian motion is a continuous-time random process used to describe the cumulative effect of pure noise. It exhibits many properties of interest, such as its martingale properties and analytical properties. In particular, the analytical properties can be extended to develop the field of stochastic analysis, which when combined with its martingale properties, has many applications in finance. The purpose of this project is to study these properties of Brownian motion in a depth greater than what is offered in undergraduate courses, as well as to explore some of the applications in financial mathematics.
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.