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

EMSW21-RTG：培训、指导

• 批准号: 0739195
• 负责人: Rene Carmona
• 金额: $ 226.88万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-02-15 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0739195&HistoricalAwards=false
• 关键词: EMSW21; RTG; Training; Mentoring; &amp

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.

本计画是关于随机分析数学的研究与教学，其动机是在许多应用领域。这些应用，其中包括金融数学、电信、风险度量分析、动态排队系统和温室气体排放，是吸引年轻人才进入随机分析的关键，这是一个在过去两年中获得许多重大数学奖项的领域。本文研究的问题所涉及的一些技术问题有：重尾分布的分析;随机偏微分方程;跳跃过程的多尺度渐近近似;集值函数的凸分析;马尔可夫服务网络时变泊松过程模型的极限定理。 随机分析工具对于核心应用数学培训至关重要，该RTG旨在培养一些未来的培训师，以及这些技能的从业者，在这一领域具有严格的基础。概率，不确定性数学方面的专业知识，在美国需求量很大：大学数学系和应用数学课程，运营和风险管理，金融监管和公共政策办公室，生物工程和电信行业。该项目的倡议旨在吸引有才华的美国学生攻读研究生学位，以及博士后职位和超越。RTG对数学方法论的教育强调意味着我们将培养具有广泛适用的技术技能的人，这些技能可能会随着工作场所需求和趋势的发展而应用于各种不同的环境。例如，在金融市场，监管不力和缺乏对所涉及风险的理解，导致了广泛的危机，如2007年夏季次级抵押贷款崩溃引发的危机，每天都在威胁着越来越多的退休和捐赠基金以及公共储蓄。我们得阻止这辆失控的火车该项目的最终目标是通过开发新的工具和策略来教育未来的科学家、政策制定者和监管者以及潜在的投资者，使他们了解风险以及描述和控制风险的数学语言。通过关注教育工作者和从业人员传统上不被注意的风险形式，例如操作风险，我们将提高认识水平，并使健全的控制成为可能。