In this paper we prove optimal interior regularity for solutions to the obstacle problem for a class of second order differential operators of Kolmogorov type. We treat smooth obstaclesas well as non-smooth obstacles. All our proofs follow the same line of thought and are based on blow-ups, compactness, barriers and arguments by contradiction. This problem arises in financial mathematics, when considering path-dependent derivative contracts with the early exercise feature.
Optimal regularity in the obstacle problem for Kolmogorov operators related to American Asian options / M., Frentz; K., Nystrom; A., Pascucci; Polidoro, Sergio. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - STAMPA. - 347:4(2010), pp. 805-838. [10.1007/s00208-009-0456-z]
Optimal regularity in the obstacle problem for Kolmogorov operators related to American Asian options
POLIDORO, Sergio
2010
Abstract
In this paper we prove optimal interior regularity for solutions to the obstacle problem for a class of second order differential operators of Kolmogorov type. We treat smooth obstaclesas well as non-smooth obstacles. All our proofs follow the same line of thought and are based on blow-ups, compactness, barriers and arguments by contradiction. This problem arises in financial mathematics, when considering path-dependent derivative contracts with the early exercise feature.
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