Invariant representation for generators of general time interval quadratic BSDEs under stochastic growth conditions

TL;DR

This paper establishes a general invariant representation theorem for generators of quadratic BSDEs over arbitrary time intervals, accommodating stochastic growth conditions, thereby unifying and extending existing results in the field.

Contribution

It introduces a novel approach to prove the invariant representation theorem for quadratic BSDE generators with stochastic growth, unifying previous results and broadening applicability.

Findings

Proves a general invariant representation theorem for quadratic BSDE generators.

Unifies existing results under a broader stochastic growth framework.

Provides a new proof technique for the representation theorem.

Abstract

This paper is devoted to proving a general invariant representation theorem for generators of general time interval backward stochastic differential equations, where the generator $g$ has a quadratic growth in the unknown variable $z$ and satisfies some stochastic growth conditions in the unknown variable $y$. This unifies and strengthens some known results. And, a natural and innovative idea is used to prove the representation theorem.