BSDEs driven by normal martingale

Abstract

The aim of this paper is to study backward stochastic differential equation driven by a class of normal martingale. We prove the existence and uniqueness results of the solution under the stochastic Lipschitz condition by mean the martingale representation theorem. In addition, we show that the solution of these equations provides a viscosity solution of the associated system with partial differential equations.

Keywords:

• Backward stochastic differential equation
• normal martingale
• stochastic Lipschitz coefficient
• viscosity solution

2010 Mathematics Subject Classifications:

• 60H20
• 60H30
• 65C30

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Center for Scientific and Technical Research (CNRST), Morocco.