Existence, uniqueness and approximation for $L^p$ solutions of reflected BSDEs under weaker assumptions

Abstract

We put forward and prove several existence and uniqueness results for $L^p(p>1)$ solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition in $y$ and a uniform continuity condition or a linear growth condition in $z$. A necessary and sufficient condition with respect to the growth of barrier is also explored to ensure the existence of a solution. And, we show that the solutions may be approximated by the penalization method and by some sequences of solutions of reflected BSDEs. Our results improve considerably some known works.

40 pages

References in corpus (3)

• L^p solutions of reflected BSDEs under monotonicity condition
• Construction and Uniqueness for reflected BSDE under linear increasing condition
• $L^p$ solutions of multidimensional BSDEs with weak monotonicity and general growth generators