Topics in Risk: Self-Normalization, Copulas , Boundary Crossing and Applications

研究者研究了涉及依赖观察的三个基础广泛的调查领域。在第一个领域，他开发了精确的概率工具，用于研究因变量中的自归一化估计量。他特别探讨了基于观测数据的长期依赖的内在特性。在第二个领域，他为相关数据中罕见事件的概率开发了基于copula的估计器，并介绍了一种评估用于预测这些事件的模型质量的方法。在第三个领域，他开发了一种（基于概率的）不完全信息下跨越边界的历史方法，并对过程到达边界所需的预期时间进行了估计。他的方法的一般性质提供了“平均时间”而不是“实际时间”的估计。正在进行敏感性研究，以量化估计的稳健性。目前正在使用广泛的自然现象数据库以及使用计算机密集的一般循环模式来校准这种方法。研究者正在开发工具，以帮助理解历史信息与自然事件发生的平均时间之间的联系。他与监管机构密切合作，开发通用质量控制工具，特别适用于银行业。他与研究生的密切互动丰富了他的工作，这些学生为一群了解新方法的不同科学家提供了培训和指导，这些科学家能够在他们的学术、公共或工业生涯中制定、发展和解决他们将遇到的问题。他的工作有可能提高公众对银行和金融机构的信心，并加强对历史数据在自然资源和风险管理中的作用的理解。

The investigator studies three broadly based areas of inquiry involving dependent observations. In the first area he develops accurate probabilistic tools for the study of self-normalized estimators in dependent variables. In particular he explores the intrinsic properties of long range dependence on the basis of the observed data. In the second area he develops copula based estimators for the probability of rare events in dependent data and introduces an approach for assessing the quality of modelsused in the prediction of these events. In the third area he develops a (probabilistically based) historical approach to boundary crossing under imperfect information and develops estimates for the expected time it takes a process to hit a boundary.The general nature of his approach provides estimates on ``average times'' rather than ``actual times''. Sensitivity studies are being performed to quantify the robustness of the estimates. The methodology is being calibrated by using extensive data banks on natural phenomena as well as by the use of computer intensive general circulation models. The investigator is developing tools to aid in the understanding of the connections between historical information and the average time for the occurrence of natural events. He works closely with regulators in the development of general quality control tools with particular application to banking. His work is enriched by close interactions with graduate students contributing to the training and mentoring of a diverse group of scientists knowledgeable in the new approaches and able to formulate, develop and solve the problems they will encounter throughout their academic, public or industrial careers. His work has the potential of improving public confidence in banking and financial institutions as well as in enhancing the understanding of the role of historical data in the management of natural resources and risks.