The research to be performed will provide a new stochastic modeling framework for a class of equilibrium problems in financial markets, and outline a novel technique for a mathematical analysis of those models. The project's long-term goal is to build a general methodology for the specification of models of stock prices from market primitives such as utility functions and the random income of financial agents, and the structure of publicly available information. While the main tools include stochastic analysis, general theory of processes and finitely-additive probability, the analysis of such problems requires the use of methods from functional and convex analysis and fixed-point theory, as well. Moreover, several other purely probabilistic and stochastic-analytic projects which emerge from various aspects of the central problem will be considered.
Formation of prices in financial markets is one of the most interesting and relevant problems at the intersection of mathematics and economics. Despite the rational character of investors in financial environment, it is extremely difficult to predict future prices of stocks, bonds, commodities or any other class of assets. However, the qualitative properties of the price-evolution of these instruments can be studied using mathematical tools and a great deal of information about them can be deduced from readily observable primitives. Such knowledge can lead to a better regulation and the increased efficiency of the financial system, as well as to a better understanding of the overall functioning of our economy.
