Second order backward stochastic differential equations under a monotonicity condition
Possamaï, Dylan (2013), Second order backward stochastic differential equations under a monotonicity condition, Stochastic Processes and their Applications, 123, 5, p. 1521–1545. http://dx.doi.org/10.1016/j.spa.2013.01.002
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/1201.1049
Journal nameStochastic Processes and their Applications
MetadataShow full item record
Abstract (EN)In a recent paper, Soner, Touzi and Zhang (2012)  have introduced a notion of second order backward stochastic differential equations (2BSDEs), which are naturally linked to a class of fully non-linear PDEs. They proved existence and uniqueness for a generator which is uniformly Lipschitz in the variables y and z. The aim of this paper is to extend these results to the case of a generator satisfying a monotonicity condition in y. More precisely, we prove existence and uniqueness for 2BSDEs with a generator which is Lipschitz in z and uniformly continuous with linear growth in y. Moreover, we emphasize throughout the paper the major difficulties and differences due to the 2BSDE framework.
Subjects / KeywordsSingular probability measures; Linear growth; Monotonicity condition; Second order backward stochastic differential equation
Showing items related by title and author.
Corrigendum for Second-order reflected backward stochastic differential equations" and "Second-order BSDEs with general reflection and game options under uncertainty" Matoussi, Anis; Possamaï, Dylan; Zhou, Chao (2017) Document de travail / Working paper