On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions

By Freddy Delbaen, Ying Hu, Adrien Richou. 2009

110 citations recorded by the source corpus.

In a previous work, P. Briand and Y. Hu proved the uniqueness among the solutions which admit every exponential moments. In this paper, we prove that uniqueness holds among solutions which admit some given exponential moments. These exponential moments are natural as they are given by the existence theorem. Thanks to this uniqueness result we can strengthen the nonlinear Feynman-Kac formula proved by P. Briand and Y. Hu.

Subfields: Applied Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4d0eaacd864763bf78063421475e77b2a0b6f64d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Adrien Richou
2. Ying Hu
3. P. Briand
4. Marie-Amélie Morlais
5. Freddy Delbaen
6. Shige Peng
7. Patrick Cheridito
8. Shanjian Tang

In Finance

1. Adrien Richou
2. P. Briand
3. Ying Hu
4. Shige Peng
5. Romuald Elie
6. Patrick Cheridito
7. Jianfeng Zhang
8. Freddy Delbaen

In Mathematical Physics

1. P. Briand
2. Ying Hu
3. Adrien Richou
4. Shige Peng

Citations in the corpus

• A simple constructive approach to quadratic BSDEs with or without delay (2013, unknown): “Richou in [11].”
• Numerical simulation of BSDEs with drivers of quadratic growth (2010, background): “Many papers deal with existence and uniqueness of solution for such BSDEs: we refe r the reader to [17, 18] when the terminal condition is bounded and [3, 4, 9] for the unbounded case.”
• A financial market with interacting investors: does an equilibrium exist? (2011, unknown): “[4] to BSDEs with unbounded terminal conditions.”
• Quadratic BSDEs with convex generators and unbounded terminal conditions (2007, methodology): “Inspired by the arguments of [4] and [11], we will develop a θ-method to our quadratic G-BSDE under the further assumption of either convexity or concavity on the generator, i.”
• Monotone stability of quadratic semimartingales with applications to unbounded general quadratic BSDEs (2011, unknown): “of any order, or in Delbaen, Hu, & Richou [13] under weaker integrability assumptions.”
• BSDEs with terminal conditions that have bounded Malliavin derivative (2012, unknown): “[9].”
• Numerical simulation of quadratic BSDEs (2013, unknown): “When the terminal condition is bounded, we refer to [7, 34, 35, 42], and, in the unbounded case, we refer to [3, 8, 9, 19, 20].”
• 7 – Backward Stochastic Differential Equations (2011, unknown): “[29] extended her result to the case of unbounded terminal condition with an additional convexity assumption on the driver.”