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Numerical Scheme for Solving Stochastic Differential Equations with g-lévy process

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Journal of Applied Mathematics and Physics 2022年第2期10卷 466-474页

作者： Jiawen Mei Yifei Xin University of Shanghai for Science and Technology Shanghai China

In this paper, we propose numerical schemes for stochastic differential equations driven by g-lévy process under the g-expectation framework. By using g-Itôformula 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.

关键词： g-lévy process g-Expectation Property SDEs Euler Scheme

Option Pricing Model Driven by g-lévy process under the g-Expectation Framework

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Journal of Applied Mathematics and Physics 2023年第1期11卷 46-54页

作者： Yingmei Xu Yang li University of Shanghai for Science and Technology Shanghai China

In this paper, we first present an option pricing model of stochastic differential equations driven by the g-lévy process under the g-expectation framework, and prove the generalized Black-Scholes equations. Then, we present the algorithm for the time-homogeneous Poisson process versus the non-time-homogeneous Poisson process. Finally, we provide an explicit solution of generalized Black-Scholes equations and simulate it numerically with Matlab software.

关键词： generalized Black-Scholes Equations g-lévy process Matlab

Black-Scholes Model under g-lévy process

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Journal of Applied Mathematics and Physics 2021年第12期9卷 3202-3210页

作者： Yifei Xin Hong Zheng University of Shanghai for Science and Technology Shanghai China

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.

关键词： g-lévy process g-Itô Formula Integro-PDE

g-lévy processes under sublinear expectations

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Probability, Uncertainty and Quantitative Risk 2021年第1期6卷 1-22页

作者： Mingshang Hu Shige Peng Zhongtai Securities Institute for Financial Studies Shandong UniversityJinan 250100ShandongChina School of Mathematics Shandong UniversityJinan 250100ShandongChina

We introduce g-lévy processes which develop the theory of processes with independent and stationary increments under the framework of sublinear *** then obtain the lévy-Khintchine formula and the existence for g-lé... 详细信息

关键词： Sublinear expectation g-normal distribution g-Brownian motion g-expectation lévy process g-lévy process g-Poisson process lévy-Khintchine formula lévy-Itôdecomposition