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In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…
We give a complete algorithm and source code for constructing what we refer to as heterotic risk models (for equities), which combine: i) granularity of an industry classification; ii) diagonality of the principal component factor…
We establish a Nash equilibrium in a market with $ N $ agents with the performance criteria of relative wealth level when the market return is unobservable. Each investor has a random prior belief on the return rate of the risky asset. The…
A new framework for portfolio diversification is introduced which goes beyond the classical mean-variance approach and portfolio allocation strategies such as risk parity. It is based on a novel concept called portfolio dimensionality that…
We study the nonparametric least squares estimator (LSE) of a multivariate convex regression function. The LSE, given as the solution to a quadratic program with $O(n^2)$ linear constraints ($n$ being the sample size), is difficult to…
We present an online approach to portfolio selection. The motivation is within the context of algorithmic trading, which demands fast and recursive updates of portfolio allocations, as new data arrives. In particular, we look at two online…
In this article we deal with the problem of portfolio allocation by enhancing network theory tools. We use the dependence structure of the correlations network in constructing some well-known risk-based models in which the estimation of…
A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy a number of desirable properties. In…
In many astrophysical settings covariance matrices of large datasets have to be determined empirically from a finite number of mock realisations. The resulting noise degrades inference and precludes it completely if there are fewer…
This paper focuses on the estimation of the sample covariance matrix from low-dimensional random projections of data known as compressive measurements. In particular, we present an unbiased estimator to extract the covariance structure from…
The sparse portfolio selection problem is one of the most famous and frequently-studied problems in the optimization and financial economics literatures. In a universe of risky assets, the goal is to construct a portfolio with maximal…
Generalized linear regressions, such as logistic regressions or Poisson regressions, are long-studied regression analysis approaches, and their applications are widely employed in various classification problems. Our study considers a…
In high-dimensions, many variable selection methods, such as the lasso, are often limited by excessive variability and rank deficiency of the sample covariance matrix. Covariance sparsity is a natural phenomenon in high-dimensional…
Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean…
Recent literature provides many computational and modeling approaches for covariance matrices estimation in a penalized Gaussian graphical models but relatively little study has been carried out on the choice of the tuning parameter. This…
This paper proposes a sparse regression method that continuously interpolates between Forward Stepwise selection (FS) and the LASSO. When tuned appropriately, our solutions are much sparser than typical LASSO fits but, unlike FS fits,…
Applications of high-dimensional regression often involve multiple sources or types of covariates. We propose methodology for this setting, emphasizing the "wide data" regime with large total dimensionality p and sample size n<<p. We focus…
More than seventy years ago Harry Markowitz formulated portfolio construction as an optimization problem that trades off expected return and risk, defined as the standard deviation of the portfolio returns. Since then the method has been…
Optimizing portfolio performance is a fundamental challenge in financial modeling, requiring the integration of advanced clustering techniques and data-driven optimization strategies. This paper introduces a comparative backtesting approach…
Covariance regression offers an effective way to model the large covariance matrix with the auxiliary similarity matrices. In this work, we propose a sparse covariance regression (SCR) approach to handle the potentially high-dimensional…