Two Theorems of Multiple G-ItôIntegral under G-Lévy Process

In this paper, according to G-Brownian motion and other related concepts and properties, we define multiple Itôintegrals driven by G-Brownian motion and G-Lévy process. By using the G-Itôformula and the properties of G-expectation, two main theorems about Itôintegral are obtained and proved. These two theorems provide powerful help for the subsequent research on jump process.

Black-Scholes Model under G-Lévy Process

In this paper, we study the option price theory of stochastic differential equations under G-Lévy process. By using G-Itô formula and G-expectation property, we give the proof of Black-Scholes equations (Integro-PDE) under G-Lévy process. Finally, we give the simulation of G-Lévy process and the explicit solution of Black-Scholes under G-Lévy process.