Second order backward stochastic differential equations under a monotonicity condition

Dylan Possamaï

Stochastic Processes and their Applications, 2013, vol. 123, issue 5, 1521-1545

Abstract: In a recent paper, Soner, Touzi and Zhang (2012) [19] 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.

Keywords: Second order backward stochastic differential equation; Monotonicity condition; Linear growth; Singular probability measures (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spa.2013.01.002

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