One-dimensional backward stochastic differential equations whose coefficient is monotonic in $y$ and non-Lipschitz in $z$

Abstract

In this paper we study one-dimensional BSDE’s whose coefficient $f$ is monotonic in $y$ and non-Lipschitz in $z$. We obtain a general existence result when $f$ has at most quadratic growth in $z$ and $ξ$ is bounded. We study the special case $f(t,y,z)=|z|^p$ where $p∈(1,2]$. Finally, we study the case $f$ has a linear growth in $z$, general growth in $y$ and $ξ$ is not necessarily bounded.