Title: Using kernel-based collocation methods to solve a delay partial differential equation with application to finance
Authors: Hossein Azari; Mojtaba Moradipour
Addresses: Department of Mathematics, Shahid Beheshti University, Tehran-1983969411, Iran ' Department of Mathematics, Lorestan University, Khorramabad-4431668151, Iran
Abstract: We consider a delay partial differential equation arising in a jump diffusion model of option pricing. Under the mean-reverting jump-diffusion model, the price of options on electricity satisfies a second order partial differential equation. In this paper, we use positive definite kernels to discretise the PDE in spatial direction and achieve a linear system of first order differential equation with respect to time. We impose homogenous boundary conditions of the PDE by using a manipulated version of kernels called 'recursive kernels'. The proposed methods are fast and accurate with low computational complexity. No integrations are necessary and the time dependent system of differential equations can be solving analytically. Illustrative example is included to demonstrate the validity and applicability of the new techniques.
Keywords: positive definite kernels; collocation methods; mesh free methods; jump diffusion models; option pricing.
International Journal of Computing Science and Mathematics, 2019 Vol.10 No.1, pp.105 - 114
Accepted: 21 Jul 2017
Published online: 30 Jan 2019 *