  This thesis consists of three parts. In the first part, we study
$\mathbb{L}^p$ solutions of a large class of BSDEs. Existence, comparison
theorem, uniqueness and a stability result are proved. In the second part, we
establish the solvability of quadratic semimartingale BSDEs. In contrast to
current literature, we use Lipschitz-quadratic regularization and obtain the
existence and uniqueness results with minimal assumptions. The third part is a
brief summary of quadratic semimartingales and the monotone stability result.
This provides an alternative proof of monotone stability result for quadratic
semimartingales BSDEs.
