Dynamic Uncertainty Modelling in Finance

Abstract

Since the 2007 financial crisis, ensuring the stability of financial markets has become a major concern in finance and economics. Many models start from a single probability measure P and assume that this probability measure remains constant over time. In financial applications, P is certainly not known - it has to be estimated. Moreover, the modern financial world faces fast changing environments and the assumption that P remains unchanged even over a relatively short time horizon turns out to be too strong. In mathematical finance, this has led to the emergence of a field known as robust finance, which systematically addresses uncertainty in financial modelling. In this project we study uncertainty in the Knightian sense for Markov processes. The report contains a detailed summary and a more in-depth description of the achieved results.