We consider the non-adapted version of a simple problem of portfolio optimization in a financial market that results from the presence of insider information. We analyze it via anticipating stochastic calculus and compare the results obtained by means of the Russo-Vallois forward, the Ayed-Kuo, and the Hitsuda-Skorokhod integrals. We compute the optimal portfolio for each of these cases with the aim of establishing a comparison between these integrals in order to clarify their potential use in this type of problem. Our results give a partial indication that, while the forward integral yields a portfolio that is financially meaningful, the Ayed-Kuo and the Hitsuda-Skorokhod integrals do not provide an appropriate investment strategy for this problem.

In [1], the emerging convergence between high-performance computing (HPC) and artificial intelligence (AI) was highlighted. At that time, the evolution of HPC hardware, with GPUs and TPUs integrating as accelerators, fueled the rise of AI with dedicated deep learning models. This trend marked the beginning of a new approach to heterogeneous architectures, which became the fundamental basis for computeintensive applications. Today, we are witnessing a new transformation within HPC. Quantum computing (QC) has emerged as a disruptive paradigm, expanding the concept of heterogeneous supercomputing architectures. Not only do traditional accelerators, such as GPUs and TPUs, remain integral to advanced computational ecosystems, but Quantum Processing Units (QPUs) are also beginning to integrate into hybrid infrastructures. The combination of classical and quantum computing represents an expanding frontier where HPC, AI, and QC converge to tackle increasingly complex problems. The recent study "Mapping the Landscape of Quantum Computing and High-Performance Computing Research Over the Last Decade" [2] reinforces this perspective by analyzing the evolution of QC and HPC over the past decade. Through bibliometric analysis and scientific mapping, this work identifies how both fields

In this paper, we address the challenge of multivariate time-series forecasting through quantum-enhanced machine learning architectures. We propose adaptation strategies that extend variational quantum circuit models (VQC), traditionally constrained to univariate data, toward the multivariate setting, exploring both purely quantum and hybrid quantum-classical formulations. First, we extend and benchmark several VQC-based and hybrid models to systematically evaluate their ability to capture cross-variable dependencies. Building on these foundations, we introduce the iQTransformer, a novel quantum transformer architecture that integrates a quantum self-attention mechanism within the iTransformer framework, enabling a quantum-native representation of inter-variable relationships. Finally, we present a comprehensive empirical evaluation on both synthetic and real-world datasets, demonstrating that quantum-enhanced models can achieve competitive or superior forecasting accuracy with fewer trainable parameters and faster convergence than state-of-the-art classical and quantum baselines. These findings highlight the potential of quantum-enhanced architectures as efficient and scalable tools for advancing multivariate time-series forecasting.