General Existence Results for Reflected BSDE and BSDE

Abstract

In this paper, we are concerned with the problem of existence of solutions for generalized reflected backward stochastic differential equations (GRBSDEs for short) and generalized backward stochastic differential equations (GBSDEs for short) when the generator $fds+gd{A}_s$ is continuous with general growth with respect to the variable $y$ and stochastic quadratic growth with respect to the variable $z$. We deal with the case of a bounded terminal condition $\xi$ and a bounded barrier $L$ as well as the case of unbounded ones. This is done by using the notion of generalized BSDEs with two reflecting barriers studied in \cite{EH}. The work is suggested by the interest the results might have in finance, control and game theory.

23 pages

References in corpus (1)

• Generalized BSDE With 2-Reflecting Barriers and Stochastic Quadratic Growth

Cited by in corpus (2)

• p-integrable solutions to multidimensional BSDEs and degenerate systems of PDEs with logarithmic nonlinearities
• Stochastic Quadratic BSDE With Two RCLL Obstacles