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Reports (Research Report) Year : 2002

Reflected BSDE's , PDE's and Variational Inequalities

Vlad Bally
  • Function : Author
M.E. Caballero
  • Function : Author
B. Fernandez
  • Function : Author
Nicole El Karoui
  • Function : Author


We discuss a class of semilinear PDE's with obstacle, of the form (_t+L)u+f(t,- x,u,^*u)+=0,uh,u_T=g where h is the obstacle. The solution of such an equation (in variational sense) is a couple (u,) where uL^2([0,T];H^1) and is a positive Radon measure concentrated on u=h. We prove that this equation has a unique solution and u is the maximal solution of the correspond- ing variational inequality. The probabilistic interpretation (Feynman-Kac formula) is given by means of Reflected Backward Stochastic Differential Equations. We give a new construction of solutions of such equations using a maximum principle. This perimts to consider obstacles with jumps.
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Dates and versions

inria-00072133 , version 1 (23-05-2006)


  • HAL Id : inria-00072133 , version 1


Vlad Bally, M.E. Caballero, B. Fernandez, Nicole El Karoui. Reflected BSDE's , PDE's and Variational Inequalities. [Research Report] RR-4455, INRIA. 2002. ⟨inria-00072133⟩
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