On the existence or non-existence of solutions for certain backward stochastic differential equations

Abstract

We investigate the existence of (local) solutions and explosions for backward stochastic differential equationswith generator | f(t,ω ,y,z)| ≤ G(y)+F(y)R(z), where G,F,R are continuous, G is increasing in {\mathbb R}₊ (decreasing in {\mathbb R}_-) and R is subquadratic. We study in detail the case f(t,ω ,y,z)=G(y)+A| z| ².