Quadratic BSDE with L2L2-terminal data: Krylov’s estimate, Itô–Krylov’s formula and existence results

Khaled Bahlali ^[1] ; Mhamed Eddahbi ^[2] ; Youssef Ouknine ^[3]
1. [1] Universite De Toulon Et Du Var
  
  Universite De Toulon Et Du Var
  
  Arrondissement de Toulon, Francia
2. [2] King Saud University
  
  King Saud University
  
  Arabia Saudí
3. [3] Cadi Ayyad University
  
  Cadi Ayyad University
  
  Marrakech-Medina, Marruecos
Mostrar afiliaciones +
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 4, 2017, págs. 2377-2397
Idioma: inglés
Enlaces
- Texto completo
Resumen
- We establish a Krylov-type estimate and an Itô–Krylov change of variable formula for the solutions of one-dimensional quadratic backward stochastic differential equations (QBSDEs) with a measurable generator and an arbitrary terminal datum. This allows us to prove various existence and uniqueness results for some classes of QBSDEs with a square integrable terminal condition and sometimes a merely measurable generator. It turns out that neither the existence of exponential moments of the terminal datum nor the continuity of the generator are necessary to the existence and/or uniqueness of solutions. We also establish a comparison theorem for solutions of a particular class of QBSDEs with measurable generator. As a byproduct, we obtain the existence of viscosity solutions for a particular class of quadratic partial differential equations (QPDEs) with a square integrable terminal datum.