Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 16
324
Views
0
CrossRef citations to date
0
Altmetric
Articles

Generalized mean-field backward stochastic differential equations and related partial differential equations

Pages 3299-3321 | Received 02 Feb 2019, Accepted 09 Jan 2020, Published online: 23 Jan 2020
 

Abstract

In this paper, we derive the existence and uniqueness of the solution for a new class of mean-field backward stochastic differential equations, which involves the integral with respect to a continuous increasing process. In addition, we study the generalized mean-field backward stochastic differential equations in a Markovian framework, that is, it is associated with a reflected McKean-Vlasov stochastic differential equation. This allows us to give a probabilistic formula for viscosity solution of a nonlocal partial differential equation with a nonlinear Neumann boundary condition.

2010 Mathematics Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the author.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.