@inproceedings{11be292899c64524856fbc5a7e384fd0,
title = "Obstacle problems for nonlocal operators",
abstract = "We prove existence, uniqueness, and regularity of viscosity solutions to the stationary and evolution obstacle problems defined by a class of nonlocal operators that are not stable-like and may have supercritical drift. We give sufficient conditions on the coefficients of the operator to obtain H{\"o}lder and Lipschitz continuous solutions. The class of nonlocal operators that we consider include non-Gaussian asset price models widely used in mathematical finance, such as Variance Gamma Processes and Regular L{\'e}vy Processes of Exponential type. In this context, the viscosity solutions that we analyze coincide with the prices of perpetual and finite expiry American options.",
keywords = "American options, And phrases. Obstacle problem, Existence and uniqueness, L{\'e}vy processes, Nonlocal operators, Viscosity solutions",
author = "Donatella Danielli and Arshak Petrosyan and Pop, {Camelia A.}",
note = "Publisher Copyright: {\textcopyright} 2019 American Mathematical Society.; AMS Special Session on New Developments in the Analysis of Nonlocal Operators, 2016 ; Conference date: 28-10-2016 Through 30-10-2016",
year = "2019",
doi = "10.1090/conm/723/14570",
language = "English (US)",
isbn = "9781470441104",
series = "Contemporary Mathematics",
publisher = "American Mathematical Society",
pages = "191--214",
editor = "Donatella Danielli and Arshak Petrosyan and Pop, {Camelia A.}",
booktitle = "New Developments in the Analysis of Nonlocal Operators",
}