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

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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.