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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…

Stock volatility prediction is an important task in the financial industry. Recent advancements in multimodal methodologies, which integrate both textual and auditory data, have demonstrated significant improvements in this domain, such as…

Using recent advances in the econometrics literature, we disentangle from high frequency observations on the transaction prices of a large sample of NYSE stocks a fundamental component and a microstructure noise component. We then relate…

The present article explores the application of randomized control techniques in empirical asset pricing and performance evaluation. It introduces geometric random walks, a class of Markov chain Monte Carlo methods, to construct flexible…

This paper resolves a pivotal open problem on nonparametric inference for nonlinear functionals of volatility matrix. Multiple prominent statistical tasks can be formulated as functionals of volatility matrix, yet a unified statistical…

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…

In machine learning, classifiers are typically susceptible to noise in the training data. In this work, we aim at reducing intra-class noise with the help of graph filtering to improve the classification performance. Considered graphs are…

Great research efforts have been devoted to exploiting deep neural networks in stock prediction. While long-range dependencies and chaotic property are still two major issues that lower the performance of state-of-the-art deep learning…

We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of…

Probabilistic error cancellation is an attempt to reverse the effect of dissipative noise channels on quantum computers by applying unphysical channels after the execution of a quantum algorithm on noisy hardware. We investigate on general…

This paper investigates the enhancement of financial time series forecasting with the use of neural networks through supervised autoencoders, aiming to improve investment strategy performance. It specifically examines the impact of noise…

We consider the problem of estimating a low-rank matrix from a noisy observed matrix. Previous work has shown that the optimal method depends crucially on the choice of loss function. In this paper, we use a family of weighted loss…

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…

Financial time series often exhibit low signal-to-noise ratio, posing significant challenges for accurate data interpretation and prediction and ultimately decision making. Generative models have gained attention as powerful tools for…

Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…

With the proliferation of algorithmic decision-making, increased scrutiny has been placed on these systems. This paper explores the relationship between the quality of the training data and the overall fairness of the models trained with…

Extracting relevant properties of empirical signals generated by nonlinear, stochastic, and high-dimensional systems is a challenge of complex systems research. Open questions are how to differentiate chaotic signals from stochastic ones,…

We formulate a discrete-time Bayesian stochastic volatility model for high-frequency stock-market data that directly accounts for microstructure noise, and outline a Markov chain Monte Carlo algorithm for parameter estimation. The methods…

We consider the problem of simulating loss probabilities and conditional excesses for linear asset portfolios under the t-copula model. Although in the literature on market risk management there are papers proposing efficient variance…

This thesis mainly focuses on two problems in capital structure and individual's life-cycle portfolio choice. In the first problem, we derive a stochastic control model to optimize banks' dividend and recapitalization policies and calibrate…