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Designing an optimum portfolio that allocates weights to its constituent stocks in a way that achieves the best trade-off between the return and the risk is a challenging research problem. The classical mean-variance theory of portfolio…
We discuss a weighted estimation of correlation and covariance matrices from historical financial data. To this end, we introduce a weighting scheme that accounts for similarity of previous market conditions to the present one. The…
This paper is devoted to study the optimal portfolio problem. Harry Markowitz's Ph.D. thesis prepared the ground for the mathematical theory of finance. In modern portfolio theory, we typically find asset returns that are modeled by a…
We consider a multi-stock continuous time incomplete market model with random coefficients. We study the investment problem in the class of strategies which do not use direct observations of the appreciation rates of the stocks, but rather…
We study high-dimensional covariance/precision matrix estimation under the assumption that the covariance/precision matrix can be decomposed into a low-rank component L and a diagonal component D. The rank of L can either be chosen to be…
Covariance matrices estimated from short, noisy, and non-Gaussian financial time series are notoriously unstable. Empirical evidence suggests that such covariance structures often exhibit power-law scaling, reflecting complex, hierarchical…
Portfolio optimization is a ubiquitous problem in financial mathematics that relies on accurate estimates of covariance matrices for asset returns. However, estimates of pairwise covariance could be better and calculating time-sensitive…
We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…
We propose an alternative linearization to the classical Markowitz quadratic portfolio optimization model, based on maximum drawdown. This model, which minimizes maximum portfolio drawdown, is particularly appealing during times of…
There has been an increasing interest in testing the equality of large Pearson's correlation matrices. However, in many applications it is more important to test the equality of large rank-based correlation matrices since they are more…
This paper investigates the large sample properties of the variance, weights, and risk of high-dimensional portfolios where the inverse of the covariance matrix of excess asset returns is estimated using a technique called nodewise…
In this work, we consider weighted signed network representations of financial markets derived from raw or denoised correlation matrices, and examine how negative edges can be exploited to reduce portfolio risk. We then propose a discrete…
This paper makes the Millennium Prize problem P vs NP operational in quantitative finance by studying cardinality-constrained portfolio selection. Starting from the convex Markowitz mean-variance program with CAPM-based expected returns (Rf…
Portfolio optimization is an important process in finance that consists in finding the optimal asset allocation that maximizes expected returns while minimizing risk. When assets are allocated in discrete units, this is a combinatorial…
We develop a rotation-invariant neural network that provides the global minimum-variance portfolio by jointly learning how to lag-transform historical returns and marginal volatilities and how to regularise the eigenvalues of large equity…
Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on Factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices…
Financial stock returns correlations have been studied in the prism of random matrix theory, to distinguish the signal from the "noise". Eigenvalues of the matrix that are above the rescaled Marchenko Pastur distribution can be interpreted…
This paper proposes analytic forms of portfolio CoVaR and CoCVaR on the normal tempered stable market model. Since CoCVaR captures the relative risk of the portfolio with respect to a benchmark return, we apply it to the relative portfolio…
Portfolio optimization under cardinality constraints transforms the classical Markowitz mean-variance problem from a convex quadratic problem into an NP-hard combinatorial optimization problem. This paper introduces a novel approach using…
This paper investigates how to measure common market risk factors using newly proposed Panel Quantile Regression Model for Returns. By exploring the fact that volatility crosses all quantiles of the return distribution and using penalized…