Multivariate Dynamic Stochastic Models of Credit Risk

本计画发展信用风险的随机模型。信贷风险指金融对手方未能履行其金融责任的风险。该项目的研究目标是开发描述信用风险的多变量随机动态的模型以及分析和计算工具，以帮助在工业实践和公共政策中实施这些模型。多个交易对手（债务人）违约到达的数学建模框架将基于马尔可夫过程的多变量随机时间变化。所提出的建模框架在应用中很重要的关键特征是，它们可以在多个债务人的违约（失败）时间之间实现任何期望水平的相关性，并且同时违约（失败）是可能的（具有正概率），从而使研究人员能够建模违约聚集现象。该项目将根据谱理论为这类模型开发一种分析方法。这将允许显式的分析计算多元违约（故障）时间分布显式计算的谱展开问题的中等规模。该项目还将开发一种模拟方法，以处理具有许多债务人的大型问题，这些问题无法通过分析谱法有效解决。如果成功的话，在这个项目中开发的随机模型和分析计算工具将有助于更好地理解和模拟金融行业的信用风险，并将有助于制定公共政策来监管金融机构。除了在金融领域的应用，该项目开发的数学建模框架和分析与计算工具还将推进通用随机建模方法，该方法适用于广泛的可靠性和故障应用，包括计算机和通信网络、电网、制造业和生物系统。

This project develops stochastic models of credit risk. Credit risk is the risk that a financial counterparty will default on its financial obligation. The research objective of the project is to develop models describing multivariate stochastic dynamics of credit risk and analytical and computational tools to help implement the models in industrial practice and public policy. The mathematical modeling framework for arrivals of defaults of multiple counterparties (obligors) will be based on multivariate random time changes of Markov processes. The key features of the proposed modeling framework important in applications are that they can achieve any desired level of correlation among default (failure) times of multiple obligors and that the simultaneous defaults (failures) are possible (have positive probability), thus enabling the researcher to model default clustering phenomena. The project will develop an analytical methodology for this class of models based on the spectral theory. This will allow explicit analytical calculations for multivariate default (failure) time distributions by explicitly computing spectral expansions in problems of moderate size. The project will also develop a simulation methodology to deal with large problems with many obligors that cannot be efficiently solved by the analytical spectral method. If successful, stochastic models and analytical and computational tools developed in this project will help better understand and model credit risk in the financial industry and will aid in the development of public policy to regulate financial institutions. In addition to applications in finance, the mathematical modeling framework and analytical and computational tools developed in the project will advance general stochastic modeling methodology that is applicable to a wide range of reliability and failure applications, including computer and communications networks, electric power grid, manufacturing, and biological systems.