Abstract
In this paper, we propose numerical schemes for stochastic differential equations driven by G-Lévy process under the G-expectation framework. By using G-Itô formula and G-expectation property, we propose Euler scheme and Milstein scheme which have order-1.0 convergence rate. And two numerical experiments including Ornstein-Uhlenbeck and Black-Scholes cases are given.
Highlights
We propose numerical schemes for stochastic differential equations driven by G-Lévy process under the G-expectation framework
By using G-Itô formula and G-expectation property, we propose Euler scheme and Milstein scheme which have order-1.0 convergence rate
We study the following stochastic differential equation driven by G-Lévy process
Summary
( ) Let’s define a sublinear expectation space Ω, , ˆ , ( ) Xt t≥0 is called a d-dimensional process if Xt ∈ d for each t ≥ 0. We will give the definition of G-Lévy process under sublinear expectation. G-Brownian motion and g s is of finite variation. We define the X as a G-Lévy process if the following properties are satisfied:. Xt and it satisfies the following form:. Where ∈ q \ {0} , Bs is a G-Brownian motion and N (de, ds) is a G-Lévy ( ) process. ( ) under which Nt t≥0 is the G-Lévy process. We define the associated discrete sublinear expectation
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