Quadratic BSDEs with convex generators and unbounded terminal conditions

Abstract

In a previous work, we proved an existence result for BSDEs with quadratic generators with respect to the variable z and with unbounded terminal conditions. However, no uniqueness result was stated in that work. The main goal of this paper is to fill this gap. In order to obtain a comparison theorem for this kind of BSDEs, we assume that the generator is convex with respect to the variable z. Under this assumption of convexity, we are also able to prove a stability result in the spirit of the a priori estimates stated in the article of N. El Karoui, S. Peng and M.-C. Quenez. With these tools in hands, we can derive the nonlinear Feynman--Kac formula in this context.

References in corpus (2)

• BSDEs with stochastic Lipschitz condition and quadratic PDEs in Hilbert spaces
• Uniqueness Results for Second Order Bellman-Isaacs Equations under Quadratic Growth Assumptions and Applications

Cited by in corpus (19)

• Numerical simulation of quadratic BSDEs
• Existence and uniqueness results for BSDEs with jumps: the whole nine yards
• Backward stochastic dynamics on a filtered probability space
• Minimal supersolutions of convex BSDEs
• Systems of ergodic BSDEs arising in regime switching forward performance processes
• The Bellman equation for power utility maximization with semimartingales
• Epstein-Zin Utility Maximization on a Random Horizon
• From Smile Asymptotics to Market Risk Measures
• A note on the existence of solutions to Markovian superquadratic BSDEs with an unbounded terminal condition
• BSDEs driven by $G$-Brownian motion with uniformly continuous generators
• Risk measures and progressive enlargement of filtration: a BSDE approach
• Solvability of a class of mean-field BSDEs with quadratic growth
• On the uniqueness of solutions to quadratic BSDEs with non-convex generators
• BSDEs in Utility Maximization with BMO Market Price of Risk
• $L^p$ solutions of finite and infinite time interval BSDEs with non-Lipschitz coefficients
• Functional inequalities for forward and backward diffusions
• A New Result for Second Order BSDEs with Quadratic Growth and its Applications
• Backward stochastic differential equations with unbounded generators
• Risk-indifference Pricing of American-style Contingent Claims