Obstacle Problems for Nonlocal Operators: A Brief Overview

Donatella Danielli, Arshak Petrosyan, Camelia A. Pop

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

Abstract

In this note, we give a brief overview of obstacle problems for nonlocal operators, focusing on the applications to financial mathematics. The class of nonlocal operators that we consider can be viewed as infinitesimal generators of non-Gaussian asset price models, such as Variance Gamma Processes and Regular Lévy Processes of Exponential type. In this context, we analyze the existence, uniqueness, and regularity of viscosity solutions to obstacle problems which correspond to prices of perpetual and finite expiry American options.

Original languageEnglish (US)
Title of host publicationNonparametric Statistics - 4th ISNPS 2018
EditorsMichele La Rocca, Brunero Liseo, Luigi Salmaso
PublisherSpringer
Pages157-172
Number of pages16
ISBN (Print)9783030573058
DOIs
StatePublished - 2020
Externally publishedYes
Event4th Conference of the International Society for Nonparametric Statistics, ISNPS 2018 - Salerno, Italy
Duration: Jun 11 2018Jun 15 2018

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume339
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference4th Conference of the International Society for Nonparametric Statistics, ISNPS 2018
CountryItaly
CitySalerno
Period6/11/186/15/18

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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