Backward stochastic differential equations driven by càdlàg martingales

Backward stochastic differential equations (BSDEs) arise in many financial problems. Although there exists a growing number of papers considering general financial markets, the theory of BSDEs has been developed just in the Brownian setting. We consider BSDEs driven by an $\mathbf{R}^d$-valued càdlàg martingale and we study the properties of the solutions in the case of a, possibly nonuniform, Lipschitz generator.