The rapid development of machine learning provides new ideas to solve the challenges in
pricing financial derivatives, which remains a major obstacle to the further development of …

In this paper, a compact scheme with three time levels is proposed to solve the partial
integro-differential equation that governs the option prices in jump-diffusion models. In the …

The accuracy and efficiency for computing option prices play very important in the financial
risk management and hedging for the investors. In this paper, we for the first time develop a …

In this paper, we study a posteriori error estimates of the IMEX BDF2 scheme for time
discretizations of solving parabolic partial integro-differential equations, which describe the …

In this paper, we first compare three different methods for approximating the first and second
derivatives from function values given at scattered points. Then we propose to use the most …

The high-order finite difference method for option pricing is one of the most popular
numerical algorithms. Therefore, it is of great significance to study its convergence rate …

The local radial basis functions (RBF) method is becoming increasingly popular as an
alternative to the global version that suffers from ill-conditioning. The purpose of this paper is …

In this research‎,‎ a new second-order finite difference scheme is proposed to solve two and
three-dimensional heat equation‎. Finite difference equations are determined via a …

The operator splitting method has been effectively applied to jump-diffusion models, and it is
also easy to implement because the differential and complementarity restrictions are …

When solving time fractional partial integro-differential equations (PIDEs) using standard
finite difference methods, we have to invert the dense matrices arising from the discretization …