Obstacle problems for nonlocal operators

Donatella Danielli, Arshak Petrosyan, Camelia A. Pop

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

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 Hölder 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 Lévy Processes of Exponential type. In this context, the viscosity solutions that we analyze coincide with the prices of perpetual and finite expiry American options.

Original languageEnglish (US)
Title of host publicationNew Developments in the Analysis of Nonlocal Operators
EditorsDonatella Danielli, Arshak Petrosyan, Camelia A. Pop
PublisherAmerican Mathematical Society
Pages191-214
Number of pages24
ISBN (Print)9781470441104
DOIs
StatePublished - 2019
EventAMS Special Session on New Developments in the Analysis of Nonlocal Operators, 2016 - Minneapolis, United States
Duration: Oct 28 2016Oct 30 2016

Publication series

NameContemporary Mathematics
Volume723
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Conference

ConferenceAMS Special Session on New Developments in the Analysis of Nonlocal Operators, 2016
Country/TerritoryUnited States
CityMinneapolis
Period10/28/1610/30/16

Keywords

  • American options
  • And phrases. Obstacle problem
  • Existence and uniqueness
  • Lévy processes
  • Nonlocal operators
  • Viscosity solutions

ASJC Scopus subject areas

  • Mathematics(all)

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