EMSW21-RTG: Training, Mentoring & Research in the Mathematics of Stochastic Analysis and Applications

Princeton University, Princeton NJ

Investigators

Abstract

This project is concerned with the research and teaching of the mathematics of stochastic analysis, motivated by a number of timely application areas. These applications, among them financial mathematics, telecommunications, risk measure analysis, dynamical queuing systems, and green-house gas emissions, are key to attracting young talent towards stochastic analysis, which is an area that has been rewarded with a number of major mathematical prizes in the past two years. Some of the technical issues arising from the problems studied here are: analysis of very heavy tailed distributions; stochastic partial differential equations; multiscale asymptotic approximations for jump processes; convex analysis for set-valued functions; limit theorems for time-changed Poisson process models of Markovian service networks. Tools of stochastic analysis are becoming crucial for a core applied mathematics training, and this RTG aims to train a number of the future trainers, as well as practitioners of the skills, with rigorous foundations in this area. Expertise in probability, the mathematics of uncertainty, is in great demand in the US: university mathematics departments and applied mathematics programs, operation and risk management, financial regulatory and public policy offices, bio-engineering, and the telecommunications industry. The initiatives of this project are designed to attract talented US students to graduate degrees, as well as postdoc positions and beyond. The RTG's educational emphasis on mathematical methodology means that we will train people with broadly applicable technical skills that may later be applied in vastly different contexts as demands and trends in the workplace evolve. In financial markets, for example, poor regulation and a lack of understanding of the risks involved, have contributed to wide-ranging crises, such as that triggered by the subprime mortgage debacle in Summer 2007, threatening more and more retirement and endowment funds and public savings every day. We need to stop this run-away train. An ultimate goal of this project is to contribute to this effort by developing new tools and strategies to educate the future scientists, policy makers and regulators, and potential investors about the risks and the mathematical language for their description and control. By focusing on forms of risk which have traditionally remained off the radar screen of educators and practitioners, e.g. operational risk, we will raise the level of awareness and make sound controls possible.