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Type: Journal article
Title: A general theory of finite state Backward Stochastic Difference Equations
Author: Cohen, S.
Elliott, R.
Citation: Stochastic Processes and their Applications, 2010; 20(4):442-466
Publisher: Elsevier Science BV
Issue Date: 2010
ISSN: 0304-4149
Statement of
Samuel N. Cohen and Robert J. Elliott
Abstract: By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions in their own right, not as approximations to the continuous case. We establish the existence and uniqueness of solutions under weaker assumptions than are needed in the continuous time setting, and also establish a comparison theorem for these solutions. The conditions of this theorem are shown to approximate those required in the continuous time setting. We also explore the relationship between the driver F and the set of solutions; in particular, we determine under what conditions the driver is uniquely determined by the solution. Applications to the theory of nonlinear expectations are explored, including a representation result. © 2010 Elsevier B.V. All rights reserved.
Keywords: BSDE
Comparison theorem
Nonlinear expectation
Dynamic risk measures
Rights: Copyright © 2010 Elsevier B.V. All rights reserved.
DOI: 10.1016/
Grant ID: ARC
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