A note on the existence of solutions to Markovian superquadratic BSDEs with an unbounded terminal condition

TL;DR

This paper extends the existence results for Markovian superquadratic backward stochastic differential equations (BSDEs) with unbounded terminal conditions by weakening the regularity assumptions on the terminal condition.

Contribution

It demonstrates that the existence of solutions holds even when the regularity assumptions on the terminal condition are less strict than previously required.

Findings

Existence of solutions under weaker regularity conditions

Extension of previous results to more general terminal conditions

Maintains uniqueness under new assumptions

Abstract

In [Stochastc Process. Appl., 122(9):3173-3208], the author proved the existence and the uniqueness of solutions to Markovian superquadratic BSDEs with an unbounded terminal condition when the generator and the terminal condition are locally Lipschitz. In this paper, we prove that the existence result remains true for these BSDEs when the regularity assumptions on the terminal condition is weakened.