Moreover, they provide limited protection in the jump-diffusion context.
Discrete jump-diffusion operator: Let Ψ u)=u+buα/2 with 0<α<2.
We need the following technical result from Bao [10] for the jump-diffusion coefficient.
(4) Discrete jump-diffusion operator: Let Ψ u)=u+buα/2 with 0<α<2.
Hence our method is efficient for the nonlinear jump-diffusion systems.
The results show that the CSSθ method is efficient for simulating the nonlinear jump-diffusion systems.
The first model, called the jump-diffusion model, was proposed by Cartea and Figueroa (2005), and is a one-factor mean-reversion jump-diffusion model, adjusted to incorporate the most important characteristics of electricity prices.
For example, Higham and Kloeden [1] studied the convergence and stability of the implicit method for jump-diffusion systems, and they further analyzed the strong convergence rates of the backward Euler method for a nonlinear jump-diffusion system [2].
First, we introduce the following technique result from Bao et al. [9] for the jump-diffusion coefficient.
In this paper, our aim is to develop a compensated split-step θ (CSSθ) method for nonlinear jump-diffusion systems.
