Mathematical Sciences- Journal Articles
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Item The role of FPGAs in Modern Option Pricing techniques: A survey(MDPI, 2024-08-12) O'Mahony, Aidan; Hanzon, Bernard; Popovici, Emanuel; Science Foundation Ireland; Intel Corporation; Dell TechnologiesIn financial computation, Field Programmable Gate Arrays (FPGAs) have emerged as a transformative technology, particularly in the domain of option pricing. This study presents the impact of Field Programmable Gate Arrays (FPGAs) on computational methods in finance, with an emphasis on option pricing. Our review examined 99 selected studies from an initial pool of 131, revealing how FPGAs substantially enhance both the speed and energy efficiency of various financial models, particularly Black–Scholes and Monte Carlo simulations. Notably, the performance gains—ranging from 270- to 5400-times faster than conventional CPU implementations—are highly dependent on the specific option pricing model employed. These findings illustrate FPGAs’ capability to efficiently process complex financial computations while consuming less energy. Despite these benefits, this paper highlights persistent challenges in FPGA design optimization and programming complexity. This study not only emphasises the potential of FPGAs to further innovate financial computing but also outlines the critical areas for future research to overcome existing barriers and fully leverage FPGA technology in future financial applications.Item Conceptual climate modelling(Elsevier B.V., 2024-07-31) Krauskopf, Bernd; Keane, Andrew; Budd, ChrisModelling the climate is notoriously difficult and generally associated with high-dimensional general circulation models that may be quite unwieldy from the mathematical perspective. At the other end of the spectrum are seemingly simple conceptual models that focus on underlying mechanisms, such as the roles of different types of delayed feedback loops and/or switching phenomena for a specific climate phenomenon. This special issue is designed to highlight the usefulness of conceptual modelling in climate. It presents a number of conceptual climate models, discusses the mathematical techniques available for their analysis, and showcases how relevant insights can be gained from them, including informing more realistic modelling of the climate.Item Feynman–Kac perturbation of C* quantum stochastic flows(Springer Nature, 2024-07-06) Belton, Alexander C. R.; Wills, Stephen J.The method of Feynman–Kac perturbation of quantum stochastic processes has a long pedigree, with the theory usually developed within the framework of processes on von Neumann algebras. In this work, the theory of operator spaces is exploited to enable a broadening of the scope to flows on C* algebras. Although the hypotheses that need to be verified in this general setting may seem numerous, we provide auxiliary results that enable this to be simplified in many of the cases which arise in practice. A wide variety of examples is provided by way of illustration.Item Nonhydrostatic internal waves in the presence of mean currents and rotation(AIP Publishing, 2024-04-17) McCarney, Jordan; Science Foundation IrelandIn this paper we present a new exact solution that represents a Pollard-like, three-dimensional, nonlinear internal wave propagating on a non-uniform zonal current in a nonhydrostatic ocean model. The solution is presented in Lagrangian coordinates, and in the process we derive a dispersion relation for the internal wave which is subjected to a perturbative analysis which reveals the existence of two distinct modes of wave motion.Item Dynamics of a time-delayed relay system(American Physical Society, 2024-01-23) Illing, Lucas; Ryan, Pierce; Amann, Andreas; Irish Research Council; McAfeeWe study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong multirhythmicity, the coexistence of many stable periodic solutions for the same values of the parameters. We present a detailed study of these periodic solutions and their bifurcations. Starting from an integrodifferential model, we show how to reduce the system to a set of finite-dimensional maps. We then demonstrate that the parameter regions of existence of periodic solutions can be understood in terms of discontinuity-induced bifurcations and their stability is determined by smooth bifurcations. Using this technique, we are able to show that slowly oscillating solutions are always stable if they exist. We also demonstrate the coexistence of stable periodic solutions with quasiperiodic solutions.