Representing filtration consistent nonlinear expectations as g-expectations in general probability spaces

Author: 

Cohen, S

Publication Date: 

1 April 2012

Journal: 

Stochastic Processes and their Applications

Last Updated: 

2021-03-21T19:30:25.027+00:00

Issue: 

4

Volume: 

122

DOI: 

10.1016/j.spa.2011.12.004

page: 

1601-1626

abstract: 

We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear expectations can be expressed as the solutions to Backward Stochastic Differential Equations with Lipschitz continuous drivers, where both the martingale and the driver terms are permitted to jump, and the martingale representation is infinite dimensional. To establish this result, we show that this domination condition is sufficient to guarantee that the comparison theorem for BSDEs will hold, and we generalise the nonlinear Doob-Meyer decomposition of Peng to a general context. © 2011 Elsevier B.V. All rights reserved.

Symplectic id: 

321126

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article