Related papers: Noisy Covariance Matrices and Portfolio Optimizati…
This paper studies a robust portfolio optimization problem under the multi-factor volatility model introduced by Christoffersen et al. (2009). The optimal strategy is derived analytically under the worst-case scenario with or without…
We introduce a new method for estimating the covariance matrix for the galaxy correlation function in surveys of large-scale structure. Our method combines simple theoretical results with a realistic characterization of the survey to…
Noisy matrix completion aims at estimating a low-rank matrix given only partial and corrupted entries. Despite substantial progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of…
Portfolio optimization emerged with the seminal paper of Markowitz (1952). The original mean-variance framework is appealing because it is very efficient from a computational point of view. However, it also has one well-established failing…
A lack of software reproducibility has become increasingly apparent in the last several years, calling into question the validity of scientific findings affected by published tools. Reproducibility issues may have numerous sources of error,…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
We present convincing empirical results on the application of Randomized Signature Methods for non-linear, non-parametric drift estimation for a multi-variate financial market. Even though drift estimation is notoriously ill defined due to…
Estimating covariance matrices is a problem of fundamental importance in multivariate statistics. In practice it is increasingly frequent to work with data matrices $X$ of dimension $n\times p$, where $p$ and $n$ are both large. Results…
This paper considers the mean variance portfolio management problem. We examine portfolios which contain both primary and derivative securities. The challenge in this context is due to portfolio's nonlinearities. The delta-gamma…
In this self-contained chapter, we revisit a fundamental problem of multivariate statistics: estimating covariance matrices from finitely many independent samples. Based on massive Multiple-Input Multiple-Output (MIMO) systems we illustrate…
Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As such, results like the well-known elliptical law are…
Classical portfolio optimization methods typically determine an optimal capital allocation through the implicit, yet critical, assumption of statistical time-invariance. Such models are inadequate for real-world markets as they employ…
It is shown that the axioms for coherent risk measures imply that whenever there is an asset in a portfolio that dominates the others in a given sample (which happens with finite probability even for large samples), then this portfolio…
Using recent advances in the econometrics literature, we disentangle from high frequency observations on the transaction prices of a large sample of NYSE stocks a fundamental component and a microstructure noise component. We then relate…
In this paper, we consider the chance constrained based uncertain portfolio optimization problem in which the uncertain parameters are stochastic in nature. The primary goal of the work is to formulate the uncertain problem into a…
Repeated use of a data sample via adaptively chosen queries can rapidly lead to overfitting, wherein the empirical evaluation of queries on the sample significantly deviates from their mean with respect to the underlying data distribution.…
We obtain general, exact formulas for the overlaps between the eigenvectors of large correlated random matrices, with additive or multiplicative noise. These results have potential applications in many different contexts, from quantum…
Many data-analysis problems involve large dense matrices that describe the covariance of stationary noise processes; the computational cost of inverting these matrices, or equivalently of solving linear systems that contain them, is often a…
We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded as a consequence of…
Portfolio optimization has long been dominated by covariance-based strategies, such as the Markowitz Mean-Variance framework. However, these approaches often fail to ensure a balanced risk structure across assets, leading to concentration…