Portfolio Optimization (PO) is a financial problem aiming to maximize the net gains while minimizing the risks in a given investment portfolio. The novelty of Quantum algorithms lies in their acclaimed potential and capability to solve complex problems given the underlying Quantum Computing (QC) inf
In portfolio optimization, decision makers face difficulties from uncertainties inherent in real-world scenarios. These uncertainties significantly influence portfolio outcomes in both classical and multi-objective Markowitz models. To address these challenges, our research explores the power of rob
Reducing financial risk is of paramount importance to investors, financial institutions, and corporations. Since the pioneering contribution of Johnson (1960), the optimal hedge ratio based on futures is regularly utilized. The current paper suggests an explicit and efficient method for testing the
With the increasing complexity of financial markets and rapid growth in data volume, traditional risk monitoring methods no longer suffice for modern financial institutions. This paper designs and optimizes a risk monitoring system based on big data and machine learning. By constructing a four-layer
This paper proposes a deep delta hedging framework for options, utilizing neural networks to learn the residuals between the hedging function and the implied Black-Scholes delta. This approach leverages the smoother properties of these residuals, enhancing deep learning performance. Utilizing ten ye
In this work, we address the optimal retirement problem in the presence of a stochastic wage, formulated as a free boundary problem. Specifically, we explore an incomplete market setting where the wage cannot be perfectly hedged through investments in the risk-free and risky assets that characterize
Representation learning has emerged as a powerful paradigm for extracting valuable latent features from complex, high-dimensional data. In financial domains, learning informative representations for assets can be used for tasks like sector classification, and risk management. However, the complex an
We present a unified framework for computing CVA sensitivities, hedging the CVA, and assessing CVA risk, using probabilistic machine learning meant as refined regression tools on simulated data, validatable by low-cost companion Monte Carlo procedures. Various notions of sensitivities are introduced
Trading is a highly competitive task that requires a combination of strategy, knowledge, and psychological fortitude. With the recent success of large language models(LLMs), it is appealing to apply the emerging intelligence of LLM agents in this competitive arena and understanding if they can outpe
In this paper, we examine the Sample Average Approximation (SAA) procedure within a framework where the Monte Carlo estimator of the expectation is biased. We also introduce Multilevel Monte Carlo (MLMC) in the SAA setup to enhance the computational efficiency of solving optimization problems. In th
We introduce the concept of set risk measures (SRMs), which are real-valued maps defined on the space of all non-empty, closed, and bounded sets of almost surely bounded random variables. Traditional risk measures typically operate on random variables, but SRMs extend this framework to sets of rando
Recently, the incorporation of both temporal features and the correlation across time series has become an effective approach in time series prediction. Spatio-Temporal Graph Neural Networks (STGNNs) demonstrate good performance on many Temporal-correlation Forecasting Problem. However, when applied
Given $μ$ and $ν$, probability measures on $\mathbb R^d$ in convex order, a Bass martingale is arguably the most natural martingale starting with law $μ$ and finishing with law $ν$. Indeed, this martingale is obtained by stretching a reference Brownian motion so as to meet the data $μ,ν$. Unless $μ$
We investigate whether large language models (LLMs) can successfully perform financial statement analysis in a way similar to a professional human analyst. We provide standardized and anonymous financial statements to GPT4 and instruct the model to analyze them to determine the direction of firms’ f
Large language models (LLMs) and their fine-tuning techniques have demonstrated superior performance in various language understanding and generation tasks. This paper explores fine-tuning LLMs for stock return forecasting with financial newsflow. In quantitative investing, return forecasting is fun
This paper solves a recursive optimal stopping problem with Poisson stopping constraints using the penalized backward stochastic differential equation (PBSDE) with jumps. Stopping in this problem is only allowed at Poisson random intervention times, and jumps play a significant role not only through
Starting from a basic model in which the dynamic of the transaction prices is a geometric Brownian motion disrupted by a microstructure white noise, corresponding to the random alternation of bids and asks, we propose moment-based estimators along with their statistical properties. We then make the
Large Language Models (LLMs) have been shown to perform well for many downstream tasks. Transfer learning can enable LLMs to acquire skills that were not targeted during pre-training. In financial contexts, LLMs can sometimes beat well-established benchmarks. This paper investigates how well LLMs pe
We present weak approximations schemes of any order for the Heston model that are obtained by using the method developed by Alfonsi and Bally (2021). This method consists in combining approximation schemes calculated on different random grids to increase the order of convergence. We apply this metho
We present the first application of modern Hopfield networks to the problem of portfolio optimization. We performed an extensive study based on combinatorial purged cross-validation over several datasets and compared our results to both traditional and deep-learning-based methods for portfolio selec