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We consider the portfolio optimization with risk measured by conditional value-at-risk, based on the stress event of chosen asset being equal to the opposite of its value-at-risk level, under the normality assumption. Solvability conditions…
We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the…
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…
Portfolio sorting is ubiquitous in the empirical finance literature, where it has been widely used to identify pricing anomalies. Despite its popularity, little attention has been paid to the statistical properties of the procedure. We…
In this paper, we study the global optimality of polynomial portfolio optimization (PPO). The PPO is a kind of portfolio selection model with high-order moments and flexible risk preference parameters. We introduce a perturbation sample…
Covariance selection seeks to estimate a covariance matrix by maximum likelihood while restricting the number of nonzero inverse covariance matrix coefficients. A single penalty parameter usually controls the tradeoff between log likelihood…
Portfolio optimization is one of the essential fields of focus in finance. There has been an increasing demand for novel computational methods in this area to compute portfolios with better returns and lower risks in recent years. We…
In this paper we estimate the mean-variance portfolio in the high-dimensional case using the recent results from the theory of random matrices. We construct a linear shrinkage estimator which is distribution-free and is optimal in the sense…
Estimation of high dimensional covariance matrices is an interesting and important research topic. In this paper, we propose a dynamic structure and develop an estimation procedure for high dimensional covariance matrices. Asymptotic…
Latent variable models are widely used in social and behavioural sciences, including education, psychology, and political science. With the increasing availability of large and complex datasets, high-dimensional latent variable models have…
Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric…
In this paper, we consider a new problem of portfolio optimization using stochastic information. In a setting where there is some uncertainty, we ask how to best select $k$ potential solutions, with the goal of optimizing the value of the…
Mathematical optimization is a powerful tool for structured decision-making across domains such as resource allocation and planning. Formulating optimization models faithful to reality, though, remains a significant bottleneck as it…
${\rm CoVaR}$ is one of the most important measures of financial systemic risks. It is defined as the risk of a financial portfolio conditional on another financial portfolio being at risk. In this paper we first develop a Monte-Carlo…
Variational quantum algorithms are poised to have significant impact on high-dimensional optimization, with applications in classical combinatorics, quantum chemistry, and condensed matter. Nevertheless, the optimization landscape of these…
Portfolio selection is the central task for assets management, but it turns out to be very challenging. Methods based on pattern matching, particularly the CORN-K algorithm, have achieved promising performance on several stock markets. A…
A new approach in stochastic optimization via the use of stochastic gradient Langevin dynamics (SGLD) algorithms, which is a variant of stochastic gradient decent (SGD) methods, allows us to efficiently approximate global minimizers of…
We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As it is well known, one can map this problem into a linear programming setting. For some values of the external…
In this paper, new results in random matrix theory are derived which allow us to construct a shrinkage estimator of the global minimum variance (GMV) portfolio when the shrinkage target is a random object. More specifically, the shrinkage…
We present a quantum algorithm for portfolio optimization. We discuss the market data input, the processing of such data via quantum operations, and the output of financially relevant results. Given quantum access to the historical record…