Ivan Guo: Stochastic Optimal Transport in Financial Mathematics

Abstract: In recent years, the field of optimal transport has attracted the attention of many high-profile mathematicians with a wide range of applications. In this talk we will discuss some of its recent applications in financial mathematics, particularly on the problems of model calibration, robust finance and portfolio optimisation. Classical topological duality results are extended to probabilistic settings, connecting stochastic control problems with non-linear partial differential equations and providing interesting practical interpretations in finance. We will also look at how numerical methods, including machine learning algorithms, can be implemented to solve these problems.