Related papers: A new weak approximation scheme of stochastic diff…
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility jump models, e.g. in Bates model. In such models the option price is determined as the solution of a partial integro-differential…
This paper investigates, a new class of fractional order Runge-Kutta (FORK) methods for numerical approximation to the solution of fractional differential equations (FDEs). By using the Caputo generalizedTaylor formula and the total…
We present a method for approximating solutions of Stochastic Differential Equations (SDEs) with arbitrary rates. This approximation is derived for bounded and measurable test functions. Specifically, we demonstrate that, leveraging the…
We develop two new sets of stable, rank-adaptive Dynamically Orthogonal Runge-Kutta (DORK) schemes that capture the high-order curvature of the nonlinear low-rank manifold. The DORK schemes asymptotically approximate the truncated singular…
A focus of recent research in quantum computing has been on developing quantum algorithms for differential equations solving using variational methods on near-term quantum devices. A promising approach involves variational algorithms, which…
Next-generation exascale machines with extreme levels of parallelism will provide massive computing resources for large scale numerical simulations of complex physical systems at unprecedented parameter ranges. However, novel numerical…
Runge-Kutta (RK) methods may exhibit order reduction when applied to certain stiff problems. While fully implicit RK schemes exist that avoid order reduction via high-stage order, DIRK (diagonally implicit Runge-Kutta) schemes are…
There exist many Runge-Kutta methods (explicit or implicit), more or less adapted to specific problems. Some of them have interesting properties, such as stability for stiff problems or symplectic capability for problems with energy…
Explicit Runge-Kutta schemes with large stable step sizes are developed for integration of high order spectral difference spatial discretization on quadrilateral grids. The new schemes permit an effective time step that is substantially…
Extended Stability Runge-Kutta (ESRK) methods are crucial for solving large-scale computational problems in science and engineering, including weather forecasting, aerodynamic analysis, and complex biological modelling. However, balancing…
We review Fujiwara's scheme, a sixth order weak approximation scheme for the numerical approximation of SDEs, and embed it into a general method to construct weak approximation schemes of order $ 2m $ for $ m \in \mathbf{N} $. Those schemes…
In this paper, we provide a new scheme for approximating the weakly efficient solution set for a class of vector optimization problems with rational objectives over a feasible set defined by finitely many polynomial inequalities. More…
Stochastic differential equation (SDE) models are the foundation for pricing and hedging financial derivatives. The drift and volatility functions in SDE models are typically chosen to be algebraic functions with a small number (less than…
In this paper, we develop a higher order symmetric partitioned Runge-Kutta method for a coupled system of differential equations on Lie groups. We start with a discussion on partitioned Runge-Kutta methods on Lie groups of arbitrary order.…
New simulation approaches to evaluating path-dependent options without matrix inversion issues nor Euler bias are evaluated. They employ three main contributions: Stochastic approximation replaces regression in the LSM algorithm; Explicit…
Electron collisions, described by stochastic differential equations (SDEs), were simulated using a second-order weak convergence algorithm. Using stochastic analysis, we constructed an SDE for energetic electrons in Lorentz plasma to…
Simulation-based techniques such as variants of stochastic Runge-Kutta are the de facto approach for inference with stochastic differential equations (SDEs) in machine learning. These methods are general-purpose and used with parametric and…
High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in…
Gamma distributed delay differential equations (DDEs) arise naturally in many modelling applications. However, appropriate numerical methods for generic Gamma distributed DDEs are not currently available. Accordingly, modellers often resort…
Sampling with Markov chain Monte Carlo methods often amounts to discretizing some continuous-time dynamics with numerical integration. In this paper, we establish the convergence rate of sampling algorithms obtained by discretizing smooth…