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This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large…
In this paper we consider the stability and convergence of numerical discretizations of the Black-Scholes partial differential equation (PDE) when complemented with the popular linear boundary condition. This condition states that the…
This paper deals with the construction of numerical stable solutions of random mean square Fisher-KPP models with advection. The construction of the numerical scheme is performed in two stages. Firstly, a semidiscretization technique…
American options are the reference instruments for the model calibration of a large and important class of single stocks. For this task, a fast and accurate pricing algorithm is indispensable. The literature mainly discusses pricing methods…
In this paper a simple, effective adaptation of Alternating Direction Implicit (ADI) time discretization schemes is proposed for the numerical pricing of American-style options under the Heston model via a partial differential…
We introduce a new approach for the numerical pricing of American options. The main idea is to choose a finite number of suitable excessive functions (randomly) and to find the smallest majorant of the gain function in the span of these…
We use the semi-discrete method, originally proposed in Halidias (2012), Semi-discrete approximations for stochastic differential equations and applications, International Journal of Computer Mathematics, 89(6), to reproduce qualitative…
This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…
When approximating the expectations of a functional of a solution to a stochastic differential equation, the numerical performance of deterministic quadrature methods, such as sparse grid quadrature and quasi-Monte Carlo (QMC) methods, may…
We consider as given a discrete time financial market with a risky asset and options written on that asset and determine both the sub- and super-hedging prices of an American option in the model independent framework of ArXiv:1305.6008. We…
This paper addresses an important gap in rigorous numerical treatments for pricing American options under correlated two-asset jump-diffusion models using the viscosity solution framework, with a particular focus on the Merton model. The…
The time dependent complex Schr\"odinger equation with cubic nonlinearity is solved by constructing differential quadrature algorithm based on sinc functions. Reduction to a coupled system of real equations enables to approach the space…
In this paper, we consider a new approach for semi-discretization in time and spatial discretization of a class of semi-linear stochastic partial differential equations (SPDEs) with multiplicative noise. The drift term of the SPDEs is only…
This paper introduces a semi-analytical method for pricing American options on assets (stocks, ETFs) that pay discrete and/or continuous dividends. The problem is notoriously complex because discrete dividends create abrupt price drops and…
This paper considers a large class of linear operator equations, including linear boundary value problems for partial differential equations, and treats them as linear recovery problems for objects from their data. Well-posedness of the…
The Allen-Cahn equation is a fundamental model for phase transitions, offering critical insights into the dynamics of interface evolution in various physical systems. This paper investigates the stability and robustness of frequently…
In this paper we are interested in the numerical solution of stochastic differential equations with non negative solutions. Our goal is to construct explicit numerical schemes that preserve positivity, even for super linear stochastic…
We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two…
The stability of classical semi-implicit scheme, and some more advanced iterative schemes recently proposed for Numerical Weather Prediction (NWP) purpose is examined. In all these schemes, the solution of the centred-implicit non-linear…