论文信息 - Functional solution about stochastic differential equation driven by $G$-Brownian motion

Functional solution about stochastic differential equation driven by $G$-Brownian motion

Peng introduced the notions of $G$-expectation and $G$-Brownian motion as well as $G$-Ito formula in 2006. The $G$-Brownian motion has many rich and new properties comparing to classical Brownian motion. In this paper, we present a method to solve stochastic differential equation driven by $G$-Brownian motion without using $G$-Ito formula. Our method is mainly depending on Frobenius's Theorem. Many classical models in mathematical finance are investigated to illustrate the method. As a by-product, this financial models are extended to the case of $G$-Brownian motion.

Defei Zhang | Ping He | Defei Zhang | P. He

[1] W. Boothby. An introduction to differentiable manifolds and Riemannian geometry , 1975 .

[2] Shige Peng,et al. Stopping times and related Itô's calculus with G-Brownian motion , 2009, 0910.3871.

[3] S. Peng. G -Expectation, G -Brownian Motion and Related Stochastic Calculus of Itô Type , 2006, math/0601035.

[4] B. Øksendal. Stochastic differential equations : an introduction with applications , 1987 .

[5] Nizar Touzi,et al. Martingale Representation Theorem for the G-Expectation , 2010 .

[6] Kiyosi Itô. Stochastic Differential Equations , 2018, The Control Systems Handbook.

[7] S. Peng,et al. Backward stochastic differential equations driven by G-Brownian motion , 2012, 1206.5889.

[8] Hani J. Doss,et al. Liens entre equations di erentielles stochastiques et ordinaires , 1977 .

[9] Shige Peng,et al. Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths , 2008, 0802.1240.

[10] Bo Zhang,et al. Martingale characterization of G-Brownian motion , 2009 .

[11] Fuqing Gao,et al. Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion , 2009 .