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 obstacles as 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.
K. Nystrom, M.F., A. Pascucci (2010). Optimal regularity in the obstacle problem for Kolmogorov operators related to American Asian options. MATHEMATISCHE ANNALEN, 347, 805-838 [10.1007/s00208-009-0456-z].
Optimal regularity in the obstacle problem for Kolmogorov operators related to American Asian options
PASCUCCI, ANDREA
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 obstacles as 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
