A general theory of finite state Backward Stochastic Difference Equations

By Samuel N. Cohen, Robert J. R. Elliott. 2008

92 citations recorded by the source corpus.

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.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/271c0804ac1052242440954decfe5507df8dc7e1

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Citations in the corpus

Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions (2008, background): “A corresponding discrete time theory is covered in the paper [5].”
Existence and Comparisons for BSDEs in general spaces (2010, methodology): “In discrete time, we have shown in [7] that a necessary and sufficient condition for the existence of a solution to the discrete BSDE is that F is invariant with respect to Z in ‖ · ‖Mt and that y → y−F (ω, t, y, z) is a bijection in y for all z, t and almost all ω.”