On $L^1$ solutions of BSDE

We consider the existence and uniqueness of $L^1$ solutions of BSDEs and reflected BSDEs. It was shown that if the generator $f$ is of sublinear growth with respect to $z$, there exists a solution for $\xi\in L^1$. Here, we... [ view full abstract ]

We consider the existence and uniqueness of $L^1$ solutions of BSDEs and reflected BSDEs. It was shown that if the generator $f$ is of sublinear growth with respect to $z$, there exists a solution for $\xi\in L^1$. Here, we show the existence and uniqueness of solutions of a linearly growing BSDE under an integrability condition on $\xi$ and $f_s^0$ uniformly with respect to a family of probability measures.