Abstract
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.
Highlights
Open AccessNowadays, many studies are interested in stochastic differential equations (SDEs).And SDEs have been widely applied to economics and finance fields, such as option pricing in stock market see [1]
Option pricing formula has developed for a long time, there are many uncertainty problems in stock market
By using G-Itô formula and G-expectation property, we prove the Integro-PDE under G-Lévy process
Summary
Many studies are interested in stochastic differential equations (SDEs). And SDEs have been widely applied to economics and finance fields, such as option pricing in stock market see [1]. Peng [3] [4] proposed the sublinear expectation space to solve the uncertainty problem. The G-Brownian motion, G-Itô formula and G-center limit theorem are proposed for us in G-expectation framework. Yang and Zhao [5] introduce the simulation of G-Brownian and G-normal distribution under G-expectation and Chai studies the option pricing for stochastic differential equation under G-framework. We study Black-Scholes model under G-Lévy process and prove the Integro-PDE by using G-Itô formula, option pricing formula and G-expectation property. In. Section 3, we propose a new theorem that gives the proof of Black-Scholes equations (Integro-PDE) under G-Lévy process.
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