Uniqueness of solutions to quadratic BSDEs with locally Lipschitz generator
Abstract
We study the uniqueness of solutions of backward stochastic differential equations (BSDEs), which generator verifies $ \vert F(t,y,z)\vert\leq \alpha_t + \beta_t\vert y\vert + \theta_t\vert z\vert + f(|y|)\vert z\vert^{2} $, where $ \alpha_t $, $ \beta_t $, $ \theta_t $ are positive processes and the function $ f $ is positive, continuous and increasing. The uniqueness of solutions of such BSDEs is derived in two situations, when $ F $ is locally Lipschitz and when $ F $ is jointly convex. As a byproduct: we show the existence of viscosity solutions to the associated semilinear partial differential equations, which can contain nonlinearity that has quadratic growth in the gradient of the solution.
Fields of Study & Subjects
Stochastic processes and financial applications
Nonlinear Partial Differential Equations
Fuzzy Systems and Optimization
Publication details
- Journal / source
- Probability Uncertainty and Quantitative Risk
- Volume
- 11
- Issue
- 1
- Pages
- 19–42
- Publication date
- 1 January 2026
- Language
- EN