Stochastic differential equations driven by $G$-Brownian motion with reflecting boundary conditions

Abstract

In this paper, we introduce the idea of stochastic integrals with respect to an increasing process in the $G$-framework and extend $G$-Itô's formula. Moreover, we study the solvability of the scalar valued stochastic differential equations driven by $G$-Brownian motion with reflecting boundary conditions (RGSDEs).

References in corpus (5)

• A theoretical framework for the pricing of contingent claims in the presence of model uncertainty
• Dual formulation of second order target problems
• On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion with integral-Lipschitz coefficients
• Pathwise Construction of Stochastic Integrals
• Second order reflected backward stochastic differential equations

Cited by in corpus (7)

• A monotone scheme for G-equations with application to the explicit convergence rate of robust central limit theorem
• On the strong Markov property for stochastic differential equations driven by $G$-Brownian motion
• Quadratic backward stochastic differential equations driven by $G$-Brownian motion: discrete solutions and approximation
• Stochastic averaging for non-Lipschitz multi-valued stochastic differential equations driven by G-Brownian motion
• Lyapunov-type conditions and stochastic differential equations driven by $G$-Brownian motion
• Local time and Tanaka formula of $G$-martingales
• Reflected Stochastic Differential Equations Driven By G-Brownian motion With Nonlinear Resistance