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

研究者研究三个基础广泛的调查领域，涉及相关的观察。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。特别是，他探讨了内在的性质的长期依赖的基础上观察到的数据。在第二个领域，他开发了基于Copula的估计，用于依赖数据中罕见事件的概率，并介绍了一种评估这些事件预测中使用的模型质量的方法。在第三个领域，他开发了一种（基于概率的）历史方法来处理不完全信息下的边界穿越，并估计了一个过程到达边界所需的预期时间。正在进行敏感性研究，以量化估计数的稳健性。目前正在利用关于自然现象的大量数据库以及利用计算机密集型大气环流模型来校准这一方法。调查员正在开发工具，以帮助了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，开发特别适用于银行业的一般质量控制工具。他的工作通过与研究生的密切互动而得到丰富，这些研究生有助于培训和指导一群了解新方法的科学家，并能够制定，开发和解决他们在学术，公共或工业职业生涯中遇到的问题。他的工作有可能提高公众对银行和金融机构的信心，并提高对历史数据在自然资源和风险管理中的作用的认识。

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.