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The automatic selection of an appropriate time step size has been considered extensively in the literature. However, most of the strategies developed operate under the assumption that the computational cost (per time step) is independent of…
Orthogonality constraints naturally appear in many machine learning problems, from principal component analysis to robust neural network training. They are usually solved using Riemannian optimization algorithms, which minimize the…
Proportional integral derivative (PID) controllers are important and widely used tools in system control. Tuning of the controller gains is a laborious task, especially for complex systems such as combustion engines. To minimize the time of…
Inference for high-dimensional hidden Markov models is challenging due to the exponential-in-dimension computational cost of calculating the likelihood. To address this issue, we introduce an innovative composite likelihood approach called…
This paper proposes a method for construction of approximate feasible primal solutions from dual ones for large-scale optimization problems possessing certain separability properties. Whereas infeasible primal estimates can typically be…
We consider a simplified version of the problem of insider trading in a financial market. We approach it by means of anticipating stochastic calculus and compare the use of the Hitsuda-Skorokhod, the Ayed-Kuo, and the Russo-Vallois forward…
Hamiltonian Monte Carlo (HMC) is a popular method in sampling. While there are quite a few works of studying this method on various aspects, an interesting question is how to choose its integration time to achieve acceleration. In this…
We present a new numerical system using classical finite elements with mesh adaptivity for computing stationary solutions of the Gross-Pitaevskii equation. The programs are written as a toolbox for FreeFem++ (www.freefem.org), a free…
Simulation of unsteady creeping flows in complex geometries has traditionally required the use of a time-stepping procedure, which is typically costly and unscalable. To reduce the cost and allow for computations at much larger scales, we…
Seismic imaging is a major challenge in geophysics with broad applications. It involves solving wave propagation equations with absorbing boundary conditions (ABC) multiple times. This drives the need for accurate and efficient numerical…
We extend the approach of Carr, Itkin and Muravey, 2021 for getting semi-analytical prices of barrier options for the time-dependent Heston model with time-dependent barriers by applying it to the so-called $\lambda$-SABR stochastic…
This paper is concerned with the development and testing of advanced time-stepping methods suited for the integration of time-accurate, real-world applications of computational fluid dynamics (CFD). The performance of several time…
L\'evy-driven Ornstein-Uhlenbeck (OU) processes represent an intriguing class of stochastic processes that have garnered interest in the energy sector for their ability to capture typical features of market dynamics. However, in the current…
One popular approach to option pricing in L\'evy models is through solving the related partial integro differential equation (PIDE). For the numerical solution of such equations powerful Galerkin methods have been put forward e.g. by Hilber…
A spectral method is described for solving coupled elliptic problems on an interior and an exterior domain. The method is formulated and tested on the two-dimensional interior Poisson and exterior Laplace problems, whose solutions and their…
The increasing adoption of Digital Assets (DAs), such as Bitcoin (BTC), rises the need for accurate option pricing models. Yet, existing methodologies fail to cope with the volatile nature of the emerging DAs. Many models have been proposed…
The use of non-translation invariant risk measures within the equal risk pricing (ERP) methodology for the valuation of financial derivatives is investigated. The ability to move beyond the class of convex risk measures considered in…
Recent work has deployed linear combinations of unitaries techniques to reduce the cost of fault-tolerant quantum simulations of correlated electron models. Here, we show that one can sometimes improve upon those results with optimized…
In this paper, we first conduct a study of the portfolio selection problem, incorporating both exogenous (proportional) and endogenous (resulting from liquidity risk, characterized by a stochastic process) transaction costs through the…
In this study, we consider a numerical implementation of the nonlinear Rosenbluth-Trubnikov collision operator for particle simulations in plasma physics in the framework of the finite element method (FEM). The relevant particle evolution…