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Reflected BSDE's , PDE's and Variational Inequalities

Vlad Bally 1 M.E. Caballero B. Fernandez Nicole El Karoui
1 MATHFI - Financial mathematics
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
Abstract : 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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Submitted on : Tuesday, May 23, 2006 - 7:52:48 PM
Last modification on : Monday, December 16, 2019 - 11:40:06 AM
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  • 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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