Free Boundary Regularity in the Parabolic Fractional Obstacle Problem

Abstract

AbstractThe parabolic obstacle problem for the fractional Laplacian naturally arises in American option models when the asset prices are driven by pure‐jump Lévy processes. In this paper we study the regularity of the free boundary. Our main result establishes that, when , the free boundary is a C1,α graph in x and t near any regular free boundary point . Furthermore, we also prove that solutions u are C1 + s in x and t near such points, with a precise expansion of the form urn:x-wiley:0010-3640:media:cpa21745:cpa21745-math-0003 with , and . © 2018 Wiley Periodicals, Inc.