The theory of Lie symmetries of partial differential equations is reasonably well understood. However, less is known about the method of Lie symmetries applied to stochastic differential equations. In particular, the heat equation is related to the Fokker–Plank equation—which describes the famous model for pricing options due to Black and Scholes. This project will investigate the extent to which Lie symmetry methods can be applied to Fokker–Plank equations to arrive at new stochastic processes from known ones – in the same way as Lie symmetries can generate new solutions of a partial differential equation.
University of Technology Sydney
Rory is a third-year studying a Bachelor of Science in Mathematics. He enjoys mathematics for itself but believes a nearby application makes it all the more fascinating. In 2020 Rory will begin his honours and he hopes that the AMSI Vacation Research Scholarship project will provide valuable experience.