Financial Applications of Random Matrix Theory: a short review

By Jean-Philippe Bouchaud, Marc Potters. 2009

171 citations recorded by the source corpus.

We discuss the applications of Random Matrix Theory in the context of financial markets and econometric models, a topic about which a considerable number of papers have been devoted to in the last decade. This mini-review is intended to guide the reader through various theoretical results (the Marcenko-Pastur spectrum and its various generalisations, random SVD, free matrices, largest eigenvalue statistics, etc.) as well as some concrete applications to portfolio optimisation and out-of-sample risk estimation.

Subfields: Economics and Econometrics

View Paper: https://www.semanticscholar.org/paper/e86abc6b417af99ff36a78ff469799bde9438d6a

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In Economics and Econometrics

Citations in the corpus

Protein Sectors: Statistical Coupling Analysis versus Conservation (2014, unknown): “analyzed this structure by looking at the top eigenvectors of the SCA matrix [18, 21].”
Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning (2018, methodology): “According to MP theory [22], for finite (N,M), and with 1 N normalization, the fluctuations at the bulk edge scale as O(M − 2 3 ):”
Cleaning large correlation matrices: tools from random matrix theory (2016, methodology): “One possible parametrization is to assume a power-law distribution of the form [28]: ρC(λ) = sA (λ+ λ0) Θ(λ− λmin), (3.”
Random matrix theory in statistics: A review (2014, unknown): “Applications of RMT in wireless communications are the focus of Coulliet and Debbah (2011) and Tulino and Verdú (2004), while for a detailed look at applications in finance one may refer to Bouchaud et al. (2003) and Bouchaud and Potters (2009).”