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

EMSW21-RTG:培训、指导

基本信息

  • 批准号:
    0739195
  • 负责人:
  • 金额:
    $ 226.88万
  • 依托单位:
  • 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

项目摘要

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.
本项目主要从事随机分析数学的研究和教学,受到多个应用领域的启发。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领域的关键。在过去两年中,随机分析领域获得了许多重要的数学奖项。从这里研究的问题中产生的一些技术问题是:对重尾分布的分析;随机偏微分方程;跳跃过程的多尺度渐近逼近集值函数的凸分析马氏服务网络时变泊松过程模型的极限定理。随机分析工具在核心应用数学训练中变得越来越重要,而这个RTG旨在培养一批未来的培训师,以及在这一领域有严格基础的技能实践者。在美国,大学数学系和应用数学专业、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,对概率和不确定性数学方面的专业知识有着巨大的需求。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,以及博士后职位和其他职位。RTG的教育重点是数学方法,这意味着我们将培养具有广泛应用的技术技能的人,这些技能以后可能会随着工作场所的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,监管不力和对相关风险缺乏了解,导致了范围广泛的危机,比如2007年夏季由次级抵押贷款崩溃引发的危机,每天都威胁着越来越多的退休基金、捐赠基金和公共储蓄。我们得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帮助未来的科学家、政策制定者、监管者和潜在投资者了解风险以及描述和控制风险的数学语言,从而为这项工作做出贡献。通过关注传统上教育工作者和从业人员不关注的风险形式,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。

项目成果

期刊论文数量(0)
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会议论文数量(0)
专利数量(0)

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Rene Carmona其他文献

Eigenfunction expansions for infinite dimensional Ornstein-Uhlenbeck processes
Stochastic Analysis and Applications 2014
随机分析与应用 2014
  • DOI:
  • 发表时间:
    2014
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Domique Bakry;Erich Bauer;Jean Bertoin;Rene Carmona;Fransois Delarue;Ana Bella Curzerio;Remi Lasselle;Alexander Davie;Joscha Diehl;Peter K. Friz;Harald Oberhauser;Yidong Dong;Ronnie Sircar;David Elworthy;Hans Follmer;Claudia Kluppelberg;Ma
  • 通讯作者:
    Ma

Rene Carmona的其他文献

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{{ truncateString('Rene Carmona', 18)}}的其他基金

Equilibria in Large Populations: Asymmetric Mean Field Games and Optimal Control
大量群体中的均衡:非对称平均场博弈和最优控制
  • 批准号:
    1716673
  • 财政年份:
    2017
  • 资助金额:
    $ 226.88万
  • 项目类别:
    Continuing Grant
Robust Methods in Mathematical Finance
数学金融中的稳健方法
  • 批准号:
    1515753
  • 财政年份:
    2015
  • 资助金额:
    $ 226.88万
  • 项目类别:
    Standard Grant
Mathematical Methods for the New Commodity & Environmental Markets
新商品的数学方法
  • 批准号:
    1211928
  • 财政年份:
    2012
  • 资助金额:
    $ 226.88万
  • 项目类别:
    Standard Grant
Mathematics of Emissions Markets: Design, Models, Analysis and Simulations
排放市场数学:设计、模型、分析和模拟
  • 批准号:
    0806591
  • 财政年份:
    2008
  • 资助金额:
    $ 226.88万
  • 项目类别:
    Standard Grant
Seminar on Stochastic Processes 2006
2006年随机过程研讨会
  • 批准号:
    0549769
  • 财政年份:
    2006
  • 资助金额:
    $ 226.88万
  • 项目类别:
    Standard Grant
FRG: Collaborative Research on Mathematical Methods for Defaultable Instruments
FRG:可违约工具数学方法的合作研究
  • 批准号:
    0456195
  • 财政年份:
    2005
  • 资助金额:
    $ 226.88万
  • 项目类别:
    Standard Grant
Workshop: Risk Management for the Deregulated Electricity Markets, Princeton University, May 16, 2003
研讨会:放松管制电力市场的风险管理,普林斯顿大学,2003 年 5 月 16 日
  • 批准号:
    0326360
  • 财政年份:
    2003
  • 资助金额:
    $ 226.88万
  • 项目类别:
    Standard Grant
Surface Motions in Random Media
随机介质中的表面运动
  • 批准号:
    9870217
  • 财政年份:
    1998
  • 资助金额:
    $ 226.88万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Stochastic Processes for Schrodinger Operators and Functional Estimation
数学科学:薛定谔算子的随机过程和函数估计
  • 批准号:
    9006596
  • 财政年份:
    1990
  • 资助金额:
    $ 226.88万
  • 项目类别:
    Standard Grant

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