Stochastic modelling of financial markets with differential information - Damiani, F V (Department of Mathematics and Applied Mathematics, 2024)
Many of the fundamental results in mathematical finance are based on the assumption that all traders have access to exactly the same information, usually assumed to be the filtration generated by the history of stock prices or the history of the underlying Brownian motion. In the last fifteen years or so, many articles in the financial mathematics literature have been concerned with using techniques of stochastic calculus to model financial markets in which different traders have access to different levels of information. This thesis aims to provide a coherent account of the various approaches that have been used to model financial markets with heterogeneously informed agents. Part I of the thesis presents a description of the two branches of stochastic analysis that are required to understand the financial models: namely, Malliavin's calculus and enlargements of filtrations. Part II applies the mathematical results of Part I to provide a comprehensive presentation of the various financial models that have been introduced in the literature.