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: 0628952
• 负责人: Jean-Pierre Fouque
• 金额: $ 17.96万
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-12-31 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0628952&HistoricalAwards=false
• 关键词: FRG; Collaborative; Research; Mathematical; Methods

Award Abstract DMS-0456195 / DMS-0455982 / DMS-0456118Rene A. Carmona and K. Ronnie Sircar, Princeton UniversityJean-Pierre Fouque, North Carolina State UniversityThaleia Zariphopoulou, University of Texas at AustinFRG: Collaborative Research on Mathematical Methods for Defaultable Instruments This project investigates problems in financial mathematics motivated by credit markets in which a major source of risk is the potential default of debtors on their payment obligations. Specifically, the problems under consideration are i) utility-indifference valuation of default risk; ii) design of instruments to optimally enhance credit worthiness; iii) asymptotic analysis of stochastic intensity models to study the time-scale content of corporate yield spreads; iv) computational issues related to the analysis of correlation between defaults across firms, modeled as large systems in interaction. The first part involves stochastic control problems related to random intensity models and infinite dimensional interest rate models. The second also overlaps and involves filtering of partially observed systems. The third uses singular and regular perturbation techniques for the class of interacting potential partial differential equations arising in this context, and the fourth uses interacting particle systems to compute probabilities which are sensitive to correlation of defaults, as well as Monte Carlo computations designed for the analysis of rare events. The intellectual merit of this project is in developing applicable scientific tools to address the particular class of optimization, design, calibration and computation issues which are essential for managing default risk.Defaultable instruments, or credit-linked derivatives, are financial securities that pay their holders amounts that are contingent on the occurrence (or not) of a default event such as the bankruptcy of a firm (or a country or municipality), non-repayment of a loan or missing a mortgage payment. The market in credit-linked derivative products has grown more than seven-fold in recent years, from $170 billion outstanding notional in 1997, to almost $1400 billion through 2001. These instruments raise new challenges in modeling, analysis, computation and estimation, some of which we propose to study here by bringing together a Focused Research Group with expertise in applied mathematics, stochastic processes and computational statistics. The broader impact of the project is in deeper understanding of credit risks, which affect people from large commercial institutions to individuals with pension funds and mortgages, and designing and correctly valuing instruments to control for it. The project is also strongly geared towards training of five graduate students and one postdoctoral associate, who will benefit enormously from interaction with all parts of the broad-based group through many meetings, and in particular a large international conference on the research area at the end of the three years. The experience gained by the PI's will be reflected in their teaching of specialist graduate and undergraduate classes, and advising Senior Thesis projects in this field. As well as the closing conference, the results of the work will be disseminated through academic and industry meetings, classes and articles written for peer-reviewed journals.

获奖摘要DMS-0456195 / DMS-0455982 / DMS-0456118 Rene A.卡莫纳和K. Ronnie Sircar，普林斯顿大学Jean-Pierre Fouque，北卡罗来纳州州立大学Thaleia Zariphopoulou，德克萨斯大学奥斯汀分校FRG：可违约工具的数学方法合作研究该项目研究信贷市场驱动的金融数学问题，其中主要风险来源是债务人潜在的违约。 具体而言，正在考虑的问题是i）违约风险的效用无差异估值; ii）最佳地提高信用价值的工具设计; iii）研究公司收益率利差的时间尺度内容的随机强度模型的渐近分析; iv）与跨公司违约之间的相关性分析相关的计算问题，建模为相互作用的大系统。 第一部分涉及与随机强度模型和无穷维利率模型相关的随机控制问题。第二个也重叠，并涉及部分观测系统的过滤。 第三个使用奇异和经常扰动技术的类相互作用的潜在的偏微分方程在这种情况下产生的，和第四个使用相互作用的粒子系统来计算概率是敏感的相关性的默认值，以及蒙特卡罗计算设计用于分析罕见的事件。 这个项目的智力价值在于开发适用的科学工具，以解决管理违约风险所必需的特定类别的优化、设计、校准和计算问题。是指向持有人支付金额的金融证券，该金额取决于违约事件的发生（或不发生），如公司破产（或国家或市），不偿还贷款或错过抵押贷款付款。 近年来，信贷挂钩衍生产品的市场增长了七倍多，从1997年的1700亿美元未偿名义价值增长到2001年的近14000亿美元。 这些工具提出了新的挑战，在建模，分析，计算和估计，其中一些我们建议在这里研究，汇集了一个重点研究小组的专业知识，应用数学，随机过程和计算统计。 该项目的更广泛影响是更深入地了解信贷风险，这些风险影响到从大型商业机构到拥有养老基金和抵押贷款的个人的人，并设计和正确评估控制这些风险的工具。该项目还大力培养五名研究生和一名博士后助理，世卫组织将通过多次会议，特别是在三年结束时举行的一次关于研究领域的大型国际会议，从与基础广泛的小组所有部分的互动中获益匪浅。 PI所获得的经验将反映在他们的专业研究生和本科生课程的教学中，并为该领域的高级论文项目提供咨询。 除了闭幕会议，工作成果将通过学术和行业会议、课程和为同行评审期刊撰写的文章传播。