It is straigtforward to solve a linear Backward SDE. i.e. $dY_t=Z_tdW_t+ aY_tdt+bZ_tdt$ with $Y_T=\xi$ (where a and b are constants, $\xi$ is bounded Randon Variable.)
How can I solve $dY_t=Z_tdW_t+ a(Y_t)^+dt +bZ_tdt $ with $Y_T=\xi$ ?
($(Y_t)^+$ means the positive part of $Y_t$)
This question is very important for me. I have got stucked in it for more than one week, after trying several methods. I will be very grateful if anyone can give me some hint about possible ways to solve it! Please, any suggestion is very important for me.
I am also interested in solving $dY_t=Z_tdW_t+ a(Y_t)^+dt +b(Z_t)^+dt $ with $Y_T=\xi$ ?
I am a starter in Backward SDE and wish to explore deeper in how to solve different BSDEs. Can anyone suggest me some related books?
Thank you so much!!