Skip to main content

Singular FBSDEs and scalar conservation laws driven by diffusion processes

Author(s): Carmona, Rene; Delarue, F

To refer to this page use:
Abstract: Motivated by earlier work on the use of fully-coupled forward-backward stochastic differential equations (henceforth FBSDEs) in the analysis of mathematical models for the CO2 emissions markets, the present study is concerned with the analysis of these equations when the generator of the forward equation has a conservative degenerate structure and the terminal condition of the backward equation is a non-smooth function of the terminal value of the forward component. We show that a general form of existence and uniqueness result still holds. When the function giving the terminal condition is binary, we also show that the flow property of the forward component of the solution can fail at the terminal time. In particular, we prove that a Dirac point mass appears in its distribution, exactly at the location of the jump of the binary function giving the terminal condition. We provide a detailed analysis of the breakdown of the Markovian representation of the solution at the terminal time. © 2012 Springer-Verlag Berlin Heidelberg.
Publication Date: 1-Oct-2013
Citation: Carmona, R, Delarue, F. (2013). Singular FBSDEs and scalar conservation laws driven by diffusion processes. Probability Theory and Related Fields, 157 (1-2), 333 - 388. doi:10.1007/s00440-012-0459-7
DOI: doi:10.1007/s00440-012-0459-7
ISSN: 0178-8051
Pages: 333 - 388
Type of Material: Journal Article
Journal/Proceeding Title: Probability Theory and Related Fields
Version: Author's manuscript

Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.