Representation theorems for generators of BSDEs with monotonic and convex growth generators

TL;DR

This paper develops representation theorems for BSDE generators with monotonic, convex, and quadratic growth conditions, providing a deeper understanding of their structure and a converse comparison theorem.

Contribution

It introduces new representation theorems for BSDE generators with specific growth conditions and establishes a converse comparison theorem, advancing theoretical understanding.

Findings

Representation theorems for generators with convex and quadratic growth

Converse comparison theorem for these BSDEs

Enhanced theoretical framework for BSDE analysis

Abstract

In this paper, we establish representation theorems for generators of backward stochastic differential equations (BSDEs in short), whose generators are monotonic and convex growth in $y$ and quadratic growth in $z$. We also obtain a converse comparison theorem for such BSDEs.