Free Probability and Random Matrix Theory for Large Portfolios (Paperback)

Paperback. Reactive PublishingModern portfolio construction operates in a high-dimensional regime where the number of assets routinely approaches or exceeds the number of observations. Classical covariance estimators break down in this setting, producing unreliable risk forecasts, distorted principal components, and unstable optimization results.This book develops the mathematical and computational framework needed to address these failures. It presents free probability and random matrix theory as practical tools for spectral analysis, covariance estimation, and risk modeling of large portfolios. Readers move from the Marchenko-Pastur law and free convolution to concrete procedures for cleaning empirical spectra, recovering population eigenvalues, and constructing robust risk measures under realistic market conditions.Core topics include: Spectral methods for high-dimensional covariance matricesFree deconvolution and eigenvalue cleaning techniquesBias-corrected estimators for portfolio risk and factor modelsApplications to covariance shrinkage, principal component analysis, and stress testingNumerical implementation considerations for realistic asset universesThe material is self-contained yet rigorous, bridging theoretical results with the requirements of quantitative portfolio management. It is written for researchers, quant developers, and advanced practitioners who need reliable tools when classical multivariate statistics no longer apply.Vincent Bisette provides a focused treatment of free probability and random matrix methods tailored to the specific challenges of large-scale financial risk modeling. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.…