Improved financial risk measurement via dependence modeling

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Improved financial risk measurement via dependence modeling In the financial and insurance industry, the measurement of risk is a crucial task for both internal decision making and external reporting. Given their potential impact on world wide regulations, risk measures and their properties are an ongoing and active area of research. My research program aims to contribute to this stream of literature and to provide a better understanding of financial and actuarial risk by bringing together concepts from three areas: dependence modeling, extreme value theory (EVT) and the theory of multivariate risk measures. The main focus of my research is to advance the recently emerged theory of multivariate risk measures that takes the dependence between different risks into account instead of treating them as independent. In this way the calculated risk measure values for each individual risk are linked together, reflecting the dependence between the risks. A first step in this direction is an in-depth understanding of the dependence between the underlying sources of randomness. Such dependencies can be represented by copula functions and directly affect multivariate risk measures that act as functionals on the joint distribution of risks. The proposal therefore aims to develop and extend copula constructions that are suitable in describing high-dimensional data encountered in contemporary data sets. Another focus of risk management are extreme losses that have potentially catastrophic outcomes. While the theory is well developed for independent losses, this assumption is not warranted for financial or actuarial losses. Of specific interest in this context is the impact of non-decaying, persistent dependence. Such a dependence structure is for example present when common underlying risk factors influence the observed variables of interest. The goal of this proposal is to further explore the impact of persistent dependence in EVT with the help of copula theory. The results will make EVT more applicable to situations with common underlying risk factors and can place results obtained under independence or decaying dependence in a broader framework. To advance the theory of multivariate risk measures I aim to further extend my results concerning multivariate geometric risk measures that have been published in two recent papers. Furthermore I will take advantage of the large statistical literature on multivariate quantiles and depth functions to construct multivariate risk measures with reasonable statistical properties. Connecting different research domains will further help to establish and boost research in multivariate risk measures. In connection with extremes I aim to investigate the newly introduced extremile risk measures in a multivariate context. For all projects the generalization of the derived results to the infinite dimensional setting is a long term goal, making the results applicable to general functional data and time series settings.