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Neural network models are widely used in solving many challenging problems, such as computer vision, personalized recommendation, and natural language processing. Those models are very computationally intensive and reach the hardware limit…

We propose post-screening portfolio selection (PS$^2$), a two-step framework for high-dimensional mean--variance investing. First, assets are screened by Lasso-type regression of a constant on excess returns without an intercept. Second,…

Hedge funds have long been viewed as a veritable "black box" of investing since outsiders may never view the exact composition of portfolio holdings. Therefore, the ability to estimate an informative set of asset weights is highly desirable…

We design an optimal strategy for investment in a portfolio of assets subject to a multiplicative Brownian motion. The strategy provides the maximal typical long-term growth rate of investor's capital. We determine the optimal fraction of…

Accurately measuring portfolio similarity is critical for a wide range of financial applications, including Exchange-traded Fund (ETF) recommendation, portfolio trading, and risk alignment. Existing similarity measures often rely on exact…

This article aims to provide a comprehensive overview of sparse optimization, with a focus on both sparse signal recovery and sparse regularization techniques. We will begin by exploring the foundations of sparse optimization, delving into…

We propose trace pursuit for model-free variable selection under the sufficient dimension reduction paradigm. Two distinct algorithms are proposed: stepwise trace pursuit and forward trace pursuit. Stepwise trace pursuit achieves selection…

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

Integer variables allow the treatment of some portfolio optimization problems in a more realistic way and introduce the possibility of adding some natural features to the model. We propose an algebraic approach to maximize the expected…

We investigate the methods that simultaneously enforce sparsity and low-rank structure in a matrix as often employed for sparse phase retrieval problems or phase calibration problems in compressive sensing. We propose a new approach for…

We discuss a method for sparse signal approximation, which is based on the correlation of the target signal with a pseudo-random signal, and uses a modification of the greedy matching pursuit algorithm. We show that this approach provides…

In this paper, we propose a machine learning algorithm for time-inconsistent portfolio optimization. The proposed algorithm builds upon neural network based trading schemes, in which the asset allocation at each time point is determined by…

Portfolio selection involves optimizing simultaneously financial goals such as risk, return and Sharpe ratio. This problem holds considerable importance in economics. However, little has been studied related to the nonconvexity of the…

Discrete optimization is a central problem in mathematical optimization with a broad range of applications, among which binary optimization and sparse optimization are two common ones. However, these problems are NP-hard and thus difficult…

Utilizing market forecasts is pivotal in optimizing portfolio selection strategies. We introduce DeepClair, a novel framework for portfolio selection. DeepClair leverages a transformer-based time-series forecasting model to predict market…

In this paper, we use replica analysis to investigate the influence of correlation among the return rates of assets on the solution of the portfolio optimization problem. We consider the behavior of the optimal solution for the case where…

We investigate an optimal investment problem with a general performance criterion which, in particular, includes discontinuous functions. Prices are modeled as diffusions and the market is incomplete. We find an explicit solution for the…

Approximate inference via information projection has been recently introduced as a general-purpose approach for efficient probabilistic inference given sparse variables. This manuscript goes beyond classical sparsity by proposing efficient…

I discuss some theoretical results with a view to motivate some practical choices in portfolio optimization. Even though the setting is not completely general (for example, the covariance matrix is assumed to be non-singular), I attempt to…

In this work, I address the issue of forming riskless hedge in the continuous time option pricing model with stochastic stock volatility. I show that it is essential to verify whether the replicating portfolio is self-financing, in order…