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https://hdl.handle.net/2440/61119
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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 1879-209X |
Statement of Responsibility: | 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/j.spa.2010.01.004 |
Grant ID: | ARC |
Published version: | http://dx.doi.org/10.1016/j.spa.2010.01.004 |
Appears in Collections: | Aurora harvest Mathematical Sciences publications |
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