Representation theorem for generators of quadratic BSDEs

TL;DR

This paper proves a general representation theorem for generators of quadratic BSDEs, enabling new results like converse comparison, uniqueness, and translation invariance of quadratic g-expectations.

Contribution

It introduces a comprehensive representation theorem for quadratic BSDE generators, advancing understanding and applications in stochastic analysis.

Findings

Established a general representation theorem for quadratic BSDE generators.

Derived a converse comparison theorem for quadratic BSDEs.

Proved uniqueness and translation invariance properties of quadratic g-expectations.

Abstract

In this paper, we establish a general representation theorem for generator of backward stochastic differential equation (BSDE), whose generator has a quadratic growth in $z$. As some applications, we obtain a general converse comparison theorem of such quadratic BSDEs and uniqueness theorem, translation invariance for quadratic $g$-expectation.