Cahiers du CEREMADE 

Unité
Mixte de Recherche du C.N.R.S. N°7534 

Abstract : This paper is devoted to continuity results of the time derivative of the solution to the onedimensional parabolic obstacle problem with variable coefficients. Under regularity assumptions on the obstacle and on the coefficients, we prove that the time derivative of the solution is continuous for almost every time. When the solution is nondecreasing in time this result holds for every time. We also give an energy criterion which characterizes the continuity of the time derivative of the solution at a point of the free boundary. Such a problem arises in the pricing of american options in generalized BlackScholes models of finance. Our results apply in financial mathematics. 





200512 

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