On the backward stochastic differential equation with generator $f(y)|z{|}^2$

Abstract

In this paper, we consider the backward stochastic differential equation (BSDE) with generator $f(y)|z{|}^2,$ where the function $f$ is defined on an open interval $D$ and locally integrable. The existence and uniqueness of bounded solutions and $L^p(p\ge 1)$ solutions of such BSDEs are obtained. Some comparison theorems and a converse comparison theorem of such BSDEs are established. As an application, we give a probabilistic interpretation of viscosity solution of quadratic PDEs.

arXiv comment20 pages, final version

References in corpus (5)

• Utility maximization in incomplete markets
• Uniqueness Results for Second Order Bellman-Isaacs Equations under Quadratic Growth Assumptions and Applications
• BSDEs driven by $|z{|}^2/y$ and applications to PDEs and decision theory
• Solving Unbounded Quadratic BSDEs by a Domination Method
• Lp Solutions of Quadratic BSDEs