Lipschitz-quadratic Regularization for Quadratic Semimartingale BSDEs

TL;DR

This paper introduces a Lipschitz-quadratic regularization method to establish existence, uniqueness, and stability results for quadratic semimartingale BSDEs under weaker conditions, advancing the theoretical understanding of these equations.

Contribution

The paper develops a novel Lipschitz-quadratic regularization approach that broadens the conditions for solvability of quadratic BSDEs, providing new theoretical insights.

Findings

Proved existence and uniqueness for Lipschitz-quadratic BSDEs.

Established a stability theorem for quadratic BSDEs.

Developed a regularization technique that weakens solvability conditions.

Abstract

We refine the solvability of quadratic semimartingale BSDEs by employing a Lipschitz-quadratic regularization procedure. In the first step, we prove an existence and uniqueness result for a class of Lipschitz-quadratic BSDEs. A corresponding stability theorem and a Lipschitz-quadratic regularization are developed to solve quadratic BSDEs. The advantage of our approach is that much weaker conditions ensure the existence and uniqueness results.