Optimal regularity in the obstacle problem for Kolmogorov operators related to American Asian options
نویسندگان
چکیده
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. The problem considered arises in financial mathematics, when considering path-dependent derivative contracts with early exercise feature. Mathematics Subject Classification (2000) 35K70 · 35R35 · 35R03 · 35H10 · 35Q91 M. Frentz · K. Nyström (B) Department of Mathematics, Umeå University, 90187 Umeå, Sweden e-mail: [email protected] M. Frentz e-mail: [email protected] A. Pascucci Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy e-mail: [email protected] S. Polidoro Dipartimento di Matematica Pura ed Applicata, Università di Modena e Reggio Emilia, Via Campi, 213/b, 4112 Modena, Italy e-mail: [email protected]
منابع مشابه
Regularity near the Initial State in the Obstacle Problem for a class of Hypoelliptic Ultraparabolic Operators
This paper is devoted to a proof of regularity, near the initial state, for solutions to the Cauchy-Dirichlet and obstacle problem for a class of second order differential operators of Kolmogorov type. The approach used here is general enough to allow us to consider smooth obstacles as well as non-smooth obstacles. 2000 Mathematics Subject classification: 35R35, 35K70, 35R03, 35Q91
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