A note on backward stochastic differential equation with generator $f(y)|z|^2$

Shiqiu Zheng, Lichao Feng

Published 2018-10-16Version 1

In this note, we consider the backward stochastic differential equation (BSDE) with generator $f(y)|z|^2,$ where the function $f$ is defined on an open set and locally integral. The existence and uniqueness of solution of such BSDE is explored for bounded or unbounded terminal variables. A comparison theorem and a converse theorem theorem of such BSDEs are obtained.