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Solomiia Dmytriv: Statistical Theory of High-Dimensional Portfolios

Today massive data sets take centre stage in almost every branch of modern human activity, including networks, finance, genetics and physics. However, analysing such data presents a challenge for statisticians and requires the development of new statistical methods capable of dealing with large-scale data. This thesis is dedicated to some selected problems driven by high-dimensional financial data sets. In particular, it covers the case of optimal portfolio asset allocation problem in a high-dimensional setting, namely when the number of assets in the portfolio and the number of observations are large and of the same order of magnitude.