Publication Cover
Stochastics
An International Journal of Probability and Stochastic Processes
Volume 89, 2017 - Issue 6-7: Proceedings of the Hammamet Conference, 19-23 October 2015
115
Views
0
CrossRef citations to date
0
Altmetric
Articles

Perron’s method for viscosity solutions of semilinear path dependent PDEs

Pages 843-867 | Received 22 Apr 2016, Accepted 18 Jul 2016, Published online: 03 Aug 2016
 

Abstract

This paper proves the existence of viscosity solutions of path dependent semilinear PDEs via Perron’s method, i.e. via showing that the supremum of viscosity subsolutions is a viscosity solution. We use the notion of viscosity solutions introduced in the work of Ekren, Keller, Touzi and Zhang which considers as test functions all those smooth processes which are tangent in mean. We also provide a comparison result for semicontinuous viscosity solutions, by using a regularization technique. As an interesting byproduct, we give a new short proof for the optimal stopping problem with semicontinuous obstacles.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the Région Ile-de-France.

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 1,425.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.