Multivariate risk modeling and applications

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This research program is concerned with the development of stochastic models and statistical inference procedures for the study of dependence between heterogeneous risks, particularly in situations where rare events could have disastrous economic consequences or affect public safety. This topic is of great importance, e.g., in insurance, finance or hydrology, where accounting for dependence between claims, assets or extreme precipitations is essential for responsible risk management.****Classical tools for analyzing multivariate data, e.g., regression, often rely on the unrealistic assumption that the joint distribution of the risks (or suitable transformations thereof) is normal. A more realistic approach consists of modeling the dependence between the risks directly through a copula. When dealing with continuous data, copulas allow for a separate treatment of the dependence between, and the marginal distributions of, the components of a random vector. In accordance with this goal, and to ensure that conclusions are robust to misspecification of the marginal distributions, estimators and goodness-of-fit tests for copulas are typically based on ranks.****The grant holder has been a contributor to the area since 1985 and will pursue his research along similar lines. Over the next 5 years, he will conceive and investigate new, flexible, and tractable stochastic models that are suitable for the analysis of large sets of dependent risks. To ensure that the proposed structures are easily interpretable and well adapted to risk management applications, he will focus on stochastic representations such as random scaling and common shock models. Applications to various fields will be considered. In particular, modeling techniques specifically adapted to reserve and aggregate claim processes occurring in the insurance industry will be developed. Rank-based inference techniques adapted to these models and other familiar structures exhibiting joint tail dependence, most notably Archimax copulas, will be designed using modern functional data analytic tools such as constrained B-spline smoothing. In addition, the grant holder will undertake an ambitious extension of rank-based inference techniques in order to be able to handle properly discrete, mixed, and otherwise non-continuous data using copula models. The empirical multi-linear extension copula will play a central role in these developments.****Overall, this work will help to change the manner in which statisticians, actuaries and other researchers model multivariate data. It will contribute to the growing statistical literature on high-dimensional dependence modeling and will have measurable impact in fields such as finance, insurance, hydrology, and risk management. All new methodology will be made accessible to practitioners through the R Project for Statistical Computing. ********