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

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This project is concerned with the research and teaching of themathematics of stochastic analysis, motivated by a number of timelyapplication areas. These applications, among them financialmathematics, telecommunications, risk measure analysis, dynamicalqueuing systems, and green-house gas emissions, are key to attractingyoung talent towards stochastic analysis, which is an area that hasbeen rewarded with a number of major mathematical prizes in the pasttwo years. Some of the technical issues arising from the problemsstudied here are: analysis of very heavy tailed distributions;stochastic partial differential equations; multiscale asymptoticapproximations for jump processes; convex analysis for set-valuedfunctions; limit theorems for time-changed Poisson process models ofMarkovian service networks. Tools of stochastic analysis are becomingcrucial for a core applied mathematics training, and this RTG aims totrain a number of the future trainers, as well as practitioners of theskills, with rigorous foundations in this area.Expertise in probability, the mathematics of uncertainty, is in greatdemand in the US: university mathematics departments and appliedmathematics programs, operation and risk management, financialregulatory and public policy offices, bio-engineering, and thetelecommunications industry. The initiatives of this project aredesigned to attract talented US students to graduate degrees, as wellas postdoc positions and beyond. The RTG's educational emphasis onmathematical methodology means that we will train people with broadlyapplicable technical skills that may later be applied in vastlydifferent contexts as demands and trends in the workplace evolve. Infinancial markets, for example, poor regulation and a lack ofunderstanding of the risks involved, have contributed to wide-rangingcrises, such as that triggered by the subprime mortgage debacle inSummer 2007, threatening more and more retirement and endowment fundsand public savings every day. We need to stop this run-away train. Anultimate goal of this project is to contribute to this effort bydeveloping new tools and strategies to educate the future scientists,policy makers and regulators, and potential investors about the risksand the mathematical language for their description and control. Byfocusing on forms of risk which have traditionally remained off theradar screen of educators and practitioners, e.g. operational risk, wewill raise the level of awareness and make sound controls possible.