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On the continuity of the time derivative of the solution to the parabolic obstacle problem with variable coefficients

Blanchet, Adrien; Dolbeault, Jean; Monneau, Régis (2006), On the continuity of the time derivative of the solution to the parabolic obstacle problem with variable coefficients, Journal de Mathématiques Pures et Appliquées, 85, 3, p. 371-414. http://dx.doi.org/10.1016/j.matpur.2005.08.007

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00004421/en/
Date
2006
Journal name
Journal de Mathématiques Pures et Appliquées
Volume
85
Number
3
Publisher
Elsevier
Pages
371-414
Publication identifier
http://dx.doi.org/10.1016/j.matpur.2005.08.007
Metadata
Show full item record
Author(s)
Blanchet, Adrien
Dolbeault, Jean cc
Monneau, Régis
Abstract (EN)
This paper is devoted to continuity results of the time derivative of the solution to the one-dimensional 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 Black-Scholes models of finance. Our results apply in financial mathematics.
Subjects / Keywords
parabolic obstacle problem; free boundary; blow-up; Liouville's result; monotonicity formula

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