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.

该项目涉及随机分析数学的研究和教学，受到许多及时应用领域的推动。这些应用程序，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，是吸引年轻人才进行随机分析的关键，该领域在过去两年中获得了许多重大数学奖项。这里研究的问题引起的一些技术问题是：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来说变得至关重要，该 RTG 旨在培训一批未来的培训师以及技能实践者，在该领域拥有严格的基础。概率（不确定性数学）方面的专业知识美国需求量很大：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。该项目的举措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及其他职位。 RTG 的教育重点是数学方法论，这意味着我们将培训具有广泛适用的技术技能的人员，这些技能随后可能会随着工作场所需求和趋势的发展而应用于截然不同的环境中。例如，在金融市场，监管不力和对所涉及风险缺乏了解，导致了大范围的危机，例如2007年夏季次贷危机引发的危机，每天都威胁着越来越多的退休金、捐赠基金和公共储蓄。我们需要阻止这列失控的火车。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投资者有关风险以及用于描述和控制风险的数学语言，从而为这一努力做出贡献。通过关注传统上不受教育者和从业者关注的风险形式，例如操作风险，我们将提高认识水平，做好控制。