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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)…
We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. In this first paper we explore the need for more general optimization tools, and consider the means by which constrained random…
As a solution towards the numerical sign problem, we propose a novel Hybrid Monte Carlo algorithm, in which molecular dynamics is performed on a continuum set of integration surfaces foliated by the antiholomorphic gradient flow ("the…
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…
Sparse index tracking is a prominent passive portfolio management strategy that constructs a sparse portfolio to track a financial index. A sparse portfolio is preferable to a full portfolio in terms of reducing transaction costs and…
Optimal capital allocation between different assets is an important financial problem, which is generally framed as the portfolio optimization problem. General models include the single-period and multi-period cases. The traditional…
Extreme multi-label classification (XMLC) is a problem of tagging an instance with a small subset of relevant labels chosen from an extremely large pool of possible labels. Large label spaces can be efficiently handled by organizing labels…
This paper addresses the problem of minimizing a convex cost function under non-negativity and equality constraints, with the aim of solving the linear unmixing problem encountered in hyperspectral imagery. This problem can be formulated as…
We study the portfolio problem of maximizing the outperformance probability over a random benchmark through dynamic trading with a fixed initial capital. Under a general incomplete market framework, this stochastic control problem can be…
We present a reinforcement learning (RL)-driven framework for optimizing block-preconditioner sizes in iterative solvers used in portfolio optimization and option pricing. The covariance matrix in portfolio optimization or the…
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…
We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to the objective function a penalty proportional to the…
The expanding number of assets offers more opportunities for investors but poses new challenges for modern portfolio management (PM). As a central plank of PM, portfolio selection by expected utility maximization (EUM) faces uncontrollable…
We study the problem of optimal portfolio selection under stochastic volatility within a continuous time reinforcement learning framework with portfolio constraints. Exploration is modeled through entropy-regularized relaxed controls, where…
In this research, we introduce a novel methodology for the index tracking problem with sparse portfolios by leveraging topological data analysis (TDA). Utilizing persistence homology to measure the riskiness of assets, we introduce a…
The affine matrix rank minimization (AMRM) problem is to find a matrix of minimum rank that satisfies a given linear system constraint. It has many applications in some important areas such as control, recommender systems, matrix completion…
Portfolio optimization has been an area that has attracted considerable attention from the financial research community. Designing a profitable portfolio is a challenging task involving precise forecasting of future stock returns and risks.…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
Optimal asset allocation is a key topic in modern finance theory. To realize the optimal asset allocation on investor's risk aversion, various portfolio construction methods have been proposed. Recently, the applications of machine learning…
This paper considers consumption and portfolio optimization problems with recursive preferences in both infinite and finite time regions. Specially, the financial market consists of a risk-free asset and a risky asset that follows a general…