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We consider the problem of estimating high-dimensional covariance matrices of $K$-populations or classes in the setting where the sample sizes are comparable to the data dimension. We propose estimating each class covariance matrix as a…
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…
Traditional approaches to portfolio optimization, often rooted in Modern Portfolio Theory and solved via quadratic programming or evolutionary algorithms, struggle with scalability or flexibility, especially in scenarios involving complex…
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…
The entropic value-at-risk (EVaR) is a new coherent risk measure, which is an upper bound for both the value-at-risk (VaR) and conditional value-at-risk (CVaR). As important properties, the EVaR is strongly monotone over its domain and…
Portfolio diversification is one of the most effective ways to minimize investment risk. Individuals and fund managers aim to create a portfolio of assets that not only have high returns but are also uncorrelated. This goal can be achieved…
In this paper we construct a shrinkage estimator of the global minimum variance (GMV) portfolio by a combination of two techniques: Tikhonov regularization and direct shrinkage of portfolio weights. More specifically, we employ a double…
We provided proof here that coefficient of variation (CV) is a direct measure of risk using an equation that has been derived here for the first time. We also presented a method to generate a stock CV based on return that strongly…
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…
Markowitz mean-variance portfolios with sample mean and covariance as input parameters feature numerous issues in practice. They perform poorly out of sample due to estimation error, they experience extreme weights together with high…
We consider the problem of selecting a portfolio of assets that provides the investor a suitable balance of expected return and risk. With respect to the seminal mean-variance model of Markowitz, we consider additional constraints on the…
A critical problem in the financial world deals with the management of risk, from regulatory risk to portfolio risk. Many such problems involve the analysis of securities modelled by complex dynamics that cannot be captured analytically,…
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…
In portfolio analysis, the traditional approach of replacing population moments with sample counterparts may lead to suboptimal portfolio choices. I show that optimal portfolio weights can be estimated using a machine learning (ML)…
We show how to reduce the problem of computing VaR and CVaR with Student T return distributions to evaluation of analytical functions of the moments. This allows an analysis of the risk properties of systems to be carefully attributed…
In this paper we present an evolutionary optimization approach to solve the risk parity portfolio selection problem. While there exist convex optimization approaches to solve this problem when long-only portfolios are considered, the…
This work aims to deal with the optimal allocation instability problem of Markowitz's modern portfolio theory in high dimensionality. We propose a combined strategy that considers covariance matrix estimators from Random Matrix Theory~(RMT)…
The paper solves the problem of optimal portfolio choice when the parameters of the asset returns distribution, like the mean vector and the covariance matrix are unknown and have to be estimated by using historical data of the asset…
Portfolio optimization is a task that investors use to determine the best allocations for their investments, and fund managers implement computational models to help guide their decisions. While one of the most common portfolio optimization…
Variable division and optimization (D\&O) is a frequently utilized algorithm design paradigm in Evolutionary Algorithms (EAs). A D\&O EA divides a variable into partial variables and then optimize them respectively. A complicated problem is…